{"id":1250,"date":"2017-10-27T16:31:46","date_gmt":"2017-10-27T16:31:46","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/the-hall-effect\/"},"modified":"2017-11-08T03:26:42","modified_gmt":"2017-11-08T03:26:42","slug":"the-hall-effect","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/the-hall-effect\/","title":{"raw":"The Hall Effect","rendered":"The Hall Effect"},"content":{"raw":"\n<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Describe the Hall effect.<\/li>\n<li>Calculate the Hall emf across a current-carrying conductor.<\/li>\n<\/ul>\n<\/div>\n<p id=\"import-auto-id1905097\">We have seen effects of a magnetic field on free-moving charges. The magnetic field also affects charges moving in a conductor. One result is the Hall effect, which has important implications and applications.<\/p>\n<p id=\"import-auto-id1525810\"><a href=\"#import-auto-id2821877\" class=\"autogenerated-content\">(Figure)<\/a> shows what happens to charges moving through a conductor in a magnetic field. The field is perpendicular to the electron drift velocity and to the width of the conductor. Note that conventional current is to the right in both parts of the figure. In part (a), electrons carry the current and move to the left. In part (b), positive charges carry the current and move to the right. Moving electrons feel a magnetic force toward one side of the conductor, leaving a net positive charge on the other side. This separation of charge <em data-effect=\"italics\">creates a voltage [latex]\\epsilon [\/latex]<\/em>, known as the <span data-type=\"term\" id=\"import-auto-id2978459\">Hall emf<\/span>, <em data-effect=\"italics\">across<\/em> the conductor. The creation of a voltage <em data-effect=\"italics\">across<\/em> a current-carrying conductor by a magnetic field is known as the <span data-type=\"term\" id=\"import-auto-id1547866\">Hall effect<\/span>, after Edwin Hall, the American physicist who discovered it in 1879.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id2821877\">\n<div class=\"bc-figcaption figcaption\">The Hall effect. (a) Electrons move to the left in this flat conductor (conventional current to the right). The magnetic field is directly out of the page, represented by circled dots; it exerts a force on the moving charges, causing a voltage  [latex]\\epsilon [\/latex], the Hall emf, across the conductor. (b) Positive charges moving to the right (conventional current also to the right) are moved to the side, producing a Hall emf of the opposite sign, [latex]\\mathrm{\u2013\\epsilon }[\/latex]. Thus, if the direction of the field and current are known, the sign of the charge carriers can be determined from the Hall effect.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1843656\" data-alt=\"Figure a shows an electron with velocity v moving toward the left. The magnetic field B is oriented out of the page. The current I is running toward the right. The force vector on the electron points downward. An illustration of the right hand rule shows the right thumb pointing left with the v vector, the fingers pointing toward 7 o\u2019clock with the B vector, the force vector on a positive charge pointing up and the force vector on a negative charge pointing down. Figure b shows a positive charge moving toward the right. The magnetic field lines are coming out of the page. The current I is running toward the right. The force on the positive charge is down. An illustration of the right hand rule shows the thumb pointing in the direction of the charge\u2019s velocity, the fingers pointing in the direction of B, and F pointing down away from the palm.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_23_06_01a.jpg\" data-media-type=\"image\/jpg\" alt=\"Figure a shows an electron with velocity v moving toward the left. The magnetic field B is oriented out of the page. The current I is running toward the right. The force vector on the electron points downward. An illustration of the right hand rule shows the right thumb pointing left with the v vector, the fingers pointing toward 7 o\u2019clock with the B vector, the force vector on a positive charge pointing up and the force vector on a negative charge pointing down. Figure b shows a positive charge moving toward the right. The magnetic field lines are coming out of the page. The current I is running toward the right. The force on the positive charge is down. An illustration of the right hand rule shows the thumb pointing in the direction of the charge\u2019s velocity, the fingers pointing in the direction of B, and F pointing down away from the palm.\" width=\"380\"><\/span><\/p><\/div>\n<p id=\"import-auto-id1550354\">One very important use of the Hall effect is to determine whether positive or negative charges carries the current. Note that in <a href=\"#import-auto-id2821877\" class=\"autogenerated-content\">(Figure)<\/a>(b), where positive charges carry the current, the Hall emf has the sign opposite to when negative charges carry the current. Historically, the Hall effect was used to show that electrons carry current in metals and it also shows that positive charges carry current in some semiconductors. The Hall effect is used today as a research tool to probe the movement of charges, their drift velocities and densities, and so on, in materials. In 1980, it was discovered that the Hall effect is quantized, an example of quantum behavior in a macroscopic object.<\/p>\n<p id=\"import-auto-id2414678\">The Hall effect has other uses that range from the determination of blood flow rate to precision measurement of magnetic field strength. To examine these quantitatively, we need an expression for the Hall emf, [latex]\\epsilon [\/latex], across a conductor. Consider the balance of forces on a moving charge in a situation where [latex]B[\/latex], [latex]v[\/latex], and [latex]l[\/latex] are mutually perpendicular, such as shown in <a href=\"#import-auto-id1648625\" class=\"autogenerated-content\">(Figure)<\/a>. Although the magnetic force moves negative charges to one side, they cannot build up without limit. The electric field caused by their separation opposes the magnetic force, [latex]F=\\text{qvB}[\/latex], and the electric force, [latex]{F}_{e}=\\text{qE}[\/latex], eventually grows to equal it. That is,<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]\\text{qE}=\\text{qvB}[\/latex]<\/div>\n<p id=\"import-auto-id1751324\">or<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]E=\\text{vB}.[\/latex]<\/div>\n<p id=\"import-auto-id1565037\">Note that the electric field [latex]E[\/latex] is uniform across the conductor because the magnetic field [latex]B[\/latex] is uniform, as is the conductor. For a uniform electric field, the relationship between electric field and voltage is [latex]E=\\epsilon \/l[\/latex], where [latex]l[\/latex] is the width of the conductor and [latex]\\epsilon [\/latex] is the Hall emf. Entering this into the last expression gives<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]\\frac{\\epsilon }{l}=\\text{vB}\\text{.}[\/latex]<\/div>\n<p id=\"import-auto-id2096508\">Solving this for the Hall emf yields<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]\\epsilon =\\text{Blv}\\phantom{\\rule{0.25em}{0ex}}\\left(B,\\phantom{\\rule{0.25em}{0ex}}v,\\phantom{\\rule{0.25em}{0ex}}\\text{and}\\phantom{\\rule{0.25em}{0ex}}l,\\phantom{\\rule{0.25em}{0ex}}\\text{mutually perpendicular}\\right),[\/latex]<\/div>\n<p id=\"import-auto-id1699325\">where [latex]\\epsilon [\/latex] is the Hall effect voltage across a conductor of width [latex]l[\/latex] through which charges move at a speed [latex]v[\/latex].<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id1648625\">\n<div class=\"bc-figcaption figcaption\">The Hall emf [latex]\\epsilon [\/latex] produces an electric force that balances the magnetic force on the moving charges. The magnetic force produces charge separation, which builds up until it is balanced by the electric force, an equilibrium that is quickly reached.<\/div>\n<p><span data-type=\"media\" data-alt=\"Diagram showing an electron moving to the left in a three-dimensional rectangular space with velocity v. The magnetic field is oriented out of the page. The electric field is down. The electric force on the charge is up while the magnetic force on the charge is down. An illustration of the right hand rule shows the thumb pointing to the left with v, the fingers out of the page with B, and the force on a positive charge up and away from the palm.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_23_06_02a.jpg\" data-media-type=\"image\/jpg\" alt=\"Diagram showing an electron moving to the left in a three-dimensional rectangular space with velocity v. The magnetic field is oriented out of the page. The electric field is down. The electric force on the charge is up while the magnetic force on the charge is down. An illustration of the right hand rule shows the thumb pointing to the left with v, the fingers out of the page with B, and the force on a positive charge up and away from the palm.\" width=\"300\"><\/span><\/p><\/div>\n<p id=\"import-auto-id1422576\">One of the most common uses of the Hall effect is in the measurement of magnetic field strength [latex]B[\/latex]. Such devices, called <em data-effect=\"italics\">Hall probes<\/em>, can be made very small, allowing fine position mapping. Hall probes can also be made very accurate, usually accomplished by careful calibration. Another application of the Hall effect is to measure fluid flow in any fluid that has free charges (most do). (See <a href=\"#import-auto-id1320873\" class=\"autogenerated-content\">(Figure)<\/a>.) A magnetic field applied perpendicular to the flow direction produces a Hall emf [latex]\\epsilon [\/latex] as shown. Note that the sign of [latex]\\epsilon [\/latex] depends not on the sign of the charges, but only on the directions of [latex]B[\/latex] and [latex]v[\/latex]. The magnitude of the Hall emf is [latex]\\epsilon =\\text{Blv}[\/latex], where [latex]l[\/latex] is the pipe diameter, so that the average velocity [latex]v[\/latex] can be determined from [latex]\\epsilon [\/latex] providing the other factors are known.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id1320873\">\n<div class=\"bc-figcaption figcaption\">The Hall effect can be used to measure fluid flow in any fluid having free charges, such as blood. The Hall emf [latex]\\epsilon [\/latex] is measured across the tube perpendicular to the applied magnetic field and is proportional to the average velocity [latex]v[\/latex].<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1542617\" data-alt=\"Diagram showing a tube with diameter l with one end between the north and south poles of a magnet. The charges are moving with velocity v within the tube and out of the page. The magnetic field B is oriented across the tube, from the north to the south pole of the magnet. The force on the charges is up for positive charges and down for negative charges. e m f = B l v.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_23_06_03a.jpg\" data-media-type=\"image\/jpg\" alt=\"Diagram showing a tube with diameter l with one end between the north and south poles of a magnet. The charges are moving with velocity v within the tube and out of the page. The magnetic field B is oriented across the tube, from the north to the south pole of the magnet. The force on the charges is up for positive charges and down for negative charges. e m f = B l v.\" width=\"350\"><\/span><\/p><\/div>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id2241844\">\n<div data-type=\"title\" class=\"title\">Calculating the Hall emf: Hall Effect for Blood Flow<\/div>\n<p id=\"import-auto-id1452723\">A Hall effect flow probe is placed on an artery, applying a 0.100-T magnetic field across it, in a setup similar to that in <a href=\"#import-auto-id1320873\" class=\"autogenerated-content\">(Figure)<\/a>. What is the Hall emf, given the vessel\u2019s inside diameter is 4.00 mm and the average blood velocity is 20.0 cm\/s?<\/p>\n<p id=\"import-auto-id2812308\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id1616771\">Because [latex]B[\/latex], [latex]v[\/latex], and [latex]l[\/latex] are mutually perpendicular, the equation [latex]\\epsilon =\\text{Blv}[\/latex] can be used to find [latex]\\epsilon [\/latex].<\/p>\n<p id=\"import-auto-id1543446\"><strong>Solution<\/strong><\/p>\n<p id=\"import-auto-id1853017\">Entering the given values for [latex]B[\/latex], [latex]v[\/latex], and <em data-effect=\"italics\">[latex]l[\/latex]<\/em> gives<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-219\">[latex]\\begin{array}{lll}\\epsilon &amp; =&amp; \\text{Blv}=\\left(\\text{0.100 T}\\right)\\left(4\\text{.}\\text{00}\u00d7{\\text{10}}^{-3}\\phantom{\\rule{0.25em}{0ex}}m\\right)\\left(0\\text{.200 m\/s}\\right)\\\\ &amp; =&amp; \\text{80.0 \u03bcV}\\end{array}[\/latex]<\/div>\n<p id=\"import-auto-id1484417\"><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id1465329\">This is the average voltage output. Instantaneous voltage varies with pulsating blood flow. The voltage is small in this type of measurement. [latex]\\epsilon [\/latex] is particularly difficult to measure, because there are voltages associated with heart action (ECG voltages) that are on the order of millivolts. In practice, this difficulty is overcome by applying an AC magnetic field, so that the Hall emf is AC with the same frequency. An amplifier can be very selective in picking out only the appropriate frequency, eliminating signals and noise at other frequencies.<\/p>\n<\/div>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id2093608\">\n<h1 data-type=\"title\">Section Summary<\/h1>\n<ul>\n<li>The Hall effect is the creation of voltage [latex]\\epsilon [\/latex], known as the Hall emf, across a current-carrying conductor by a magnetic field. <\/li>\n<li>The Hall emf is given by\n<div data-type=\"equation\" class=\"equation\" id=\"eip-id2017144\">[latex]\\epsilon =\\text{Blv}\\phantom{\\rule{0.25em}{0ex}}\\left(B,\\phantom{\\rule{0.25em}{0ex}}v,\\phantom{\\rule{0.25em}{0ex}}\\text{and}\\phantom{\\rule{0.25em}{0ex}}l,\\phantom{\\rule{0.25em}{0ex}}\\text{mutually perpendicular}\\right)[\/latex]<\/div>\n<p>for a conductor of width <em data-effect=\"italics\">[latex]l[\/latex]<\/em> through which charges move at a speed [latex]v[\/latex].<\/p><\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id1523583\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1564685\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2098332\">\n<p id=\"import-auto-id1616406\">Discuss how the Hall effect could be used to obtain information on free charge density in a conductor. (Hint: Consider how drift velocity and current are related.)<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" id=\"fs-id1544499\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2114109\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2025369\">\n<p id=\"import-auto-id1416915\">A large water main is 2.50 m in diameter and the average water velocity is 6.00 m\/s. Find the Hall voltage produced if the pipe runs perpendicular to the Earth\u2019s [latex]5\\text{.}\\text{00}\u00d7{\\text{10}}^{-5}\\text{-T}[\/latex] field.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1399045\">\n<p id=\"import-auto-id1773192\">[latex]7\\text{.}\\text{50}\u00d7{\\text{10}}^{-4}\\phantom{\\rule{0.25em}{0ex}}V[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1540519\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1907612\">\n<p id=\"import-auto-id1988652\">What Hall voltage is produced by a 0.200-T field applied across a 2.60-cm-diameter aorta when blood velocity is 60.0 cm\/s?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1527365\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1066850\">\n<p id=\"import-auto-id2025116\">(a) What is the speed of a supersonic aircraft with a 17.0-m wingspan, if it experiences a 1.60-V Hall voltage between its wing tips when in level flight over the north magnetic pole, where the Earth\u2019s field strength is [latex]8\\text{.}\\text{00}\u00d7{\\text{10}}^{-5}\\phantom{\\rule{0.25em}{0ex}}\\text{T?}[\/latex] (b) Explain why very little current flows as a result of this Hall voltage.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\">\n<p id=\"import-auto-id2229613\">(a) 1.18 \u00d7 10 <sup>3<\/sup> m\/s<\/p>\n<p id=\"import-auto-id1377755\">(b) Once established, the Hall emf pushes charges one direction and the magnetic force acts in the opposite direction resulting in no net force on the charges. Therefore, no current flows in the direction of the Hall emf. This is the same as in a current-carrying conductor\u2014current does not flow in the direction of the Hall emf.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2835315\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2295527\">\n<p id=\"import-auto-id2164253\">A nonmechanical water meter could utilize the Hall effect by applying a magnetic field across a metal pipe and measuring the Hall voltage produced. What is the average fluid velocity in a 3.00-cm-diameter pipe, if a 0.500-T field across it creates a 60.0-mV Hall voltage?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1645693\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1993134\">\n<p id=\"import-auto-id1744711\">Calculate the Hall voltage induced on a patient\u2019s heart while being scanned by an MRI unit. Approximate the conducting path on the heart wall by a wire 7.50 cm long that moves at 10.0 cm\/s perpendicular to a 1.50-T magnetic field.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1529856\">\n<p id=\"import-auto-id1747279\">11.3 mV<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id976138\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1495708\">\n<p id=\"import-auto-id1158161\">A Hall probe calibrated to read [latex]1\\text{.}\\text{00 \u03bcV}[\/latex] when placed in a 2.00-T field is placed in a 0.150-T field. What is its output voltage?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1797808\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1733233\">\n<p id=\"import-auto-id2194387\">Using information in <a href=\"\/contents\/a5e2058d-3bf0-4538-9e0d-d72e24a9acfd@7#fs-id1889050\" class=\"autogenerated-content\">(Figure)<\/a>, what would the Hall voltage be if a 2.00-T field is applied across a 10-gauge copper wire (2.588 mm in diameter) carrying a 20.0-A current?\n<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1399884\">\n<p id=\"import-auto-id2080944\">[latex]1.\\text{16 \u03bcV}[\/latex]<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1442567\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2084601\">\n<p id=\"import-auto-id1347796\">Show that the Hall voltage across wires made of the same material, carrying identical currents, and subjected to the same magnetic field is inversely proportional to their diameters. (Hint: Consider how drift velocity depends on wire diameter.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"eip-id1890293\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"eip-id1890296\">\n<p id=\"eip-id1890298\">A patient with a pacemaker is mistakenly being scanned for an MRI image. A 10.0-cm-long section of pacemaker wire moves at a speed of 10.0 cm\/s perpendicular to the MRI unit\u2019s magnetic field and a 20.0-mV Hall voltage is induced. What is the magnetic field strength?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"eip-id1890305\">\n<p id=\"eip-id1890307\">2.00 T<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl class=\"definition\" id=\"import-auto-id1648144\">\n<dt>Hall effect<\/dt>\n<dd id=\"fs-id1981047\">the creation of voltage across a current-carrying conductor by a magnetic field<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2654894\">\n<dt>Hall emf<\/dt>\n<dd>the electromotive force created by a current-carrying conductor by a magnetic field, [latex]\\epsilon =\\text{Blv}[\/latex]<\/dd>\n<\/dl>\n<\/div>\n\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Describe the Hall effect.<\/li>\n<li>Calculate the Hall emf across a current-carrying conductor.<\/li>\n<\/ul>\n<\/div>\n<p id=\"import-auto-id1905097\">We have seen effects of a magnetic field on free-moving charges. The magnetic field also affects charges moving in a conductor. One result is the Hall effect, which has important implications and applications.<\/p>\n<p id=\"import-auto-id1525810\"><a href=\"#import-auto-id2821877\" class=\"autogenerated-content\">(Figure)<\/a> shows what happens to charges moving through a conductor in a magnetic field. The field is perpendicular to the electron drift velocity and to the width of the conductor. Note that conventional current is to the right in both parts of the figure. In part (a), electrons carry the current and move to the left. In part (b), positive charges carry the current and move to the right. Moving electrons feel a magnetic force toward one side of the conductor, leaving a net positive charge on the other side. This separation of charge <em data-effect=\"italics\">creates a voltage <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/><\/em>, known as the <span data-type=\"term\" id=\"import-auto-id2978459\">Hall emf<\/span>, <em data-effect=\"italics\">across<\/em> the conductor. The creation of a voltage <em data-effect=\"italics\">across<\/em> a current-carrying conductor by a magnetic field is known as the <span data-type=\"term\" id=\"import-auto-id1547866\">Hall effect<\/span>, after Edwin Hall, the American physicist who discovered it in 1879.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id2821877\">\n<div class=\"bc-figcaption figcaption\">The Hall effect. (a) Electrons move to the left in this flat conductor (conventional current to the right). The magnetic field is directly out of the page, represented by circled dots; it exerts a force on the moving charges, causing a voltage  <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/>, the Hall emf, across the conductor. (b) Positive charges moving to the right (conventional current also to the right) are moved to the side, producing a Hall emf of the opposite sign, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4bc56fce6c89eb4f3cf5592bc31d97d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#45;&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"20\" style=\"vertical-align: 0px;\" \/>. Thus, if the direction of the field and current are known, the sign of the charge carriers can be determined from the Hall effect.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1843656\" data-alt=\"Figure a shows an electron with velocity v moving toward the left. The magnetic field B is oriented out of the page. The current I is running toward the right. The force vector on the electron points downward. An illustration of the right hand rule shows the right thumb pointing left with the v vector, the fingers pointing toward 7 o\u2019clock with the B vector, the force vector on a positive charge pointing up and the force vector on a negative charge pointing down. Figure b shows a positive charge moving toward the right. The magnetic field lines are coming out of the page. The current I is running toward the right. The force on the positive charge is down. An illustration of the right hand rule shows the thumb pointing in the direction of the charge\u2019s velocity, the fingers pointing in the direction of B, and F pointing down away from the palm.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_23_06_01a.jpg\" data-media-type=\"image\/jpg\" alt=\"Figure a shows an electron with velocity v moving toward the left. The magnetic field B is oriented out of the page. The current I is running toward the right. The force vector on the electron points downward. An illustration of the right hand rule shows the right thumb pointing left with the v vector, the fingers pointing toward 7 o\u2019clock with the B vector, the force vector on a positive charge pointing up and the force vector on a negative charge pointing down. Figure b shows a positive charge moving toward the right. The magnetic field lines are coming out of the page. The current I is running toward the right. The force on the positive charge is down. An illustration of the right hand rule shows the thumb pointing in the direction of the charge\u2019s velocity, the fingers pointing in the direction of B, and F pointing down away from the palm.\" width=\"380\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id1550354\">One very important use of the Hall effect is to determine whether positive or negative charges carries the current. Note that in <a href=\"#import-auto-id2821877\" class=\"autogenerated-content\">(Figure)<\/a>(b), where positive charges carry the current, the Hall emf has the sign opposite to when negative charges carry the current. Historically, the Hall effect was used to show that electrons carry current in metals and it also shows that positive charges carry current in some semiconductors. The Hall effect is used today as a research tool to probe the movement of charges, their drift velocities and densities, and so on, in materials. In 1980, it was discovered that the Hall effect is quantized, an example of quantum behavior in a macroscopic object.<\/p>\n<p id=\"import-auto-id2414678\">The Hall effect has other uses that range from the determination of blood flow rate to precision measurement of magnetic field strength. To examine these quantitatively, we need an expression for the Hall emf, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/>, across a conductor. Consider the balance of forces on a moving charge in a situation where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef71511c70f0e4b25cc6bd69f3bc20c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-502276c66966e5a861539c7de60c26c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#108;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"5\" style=\"vertical-align: 0px;\" \/> are mutually perpendicular, such as shown in <a href=\"#import-auto-id1648625\" class=\"autogenerated-content\">(Figure)<\/a>. Although the magnetic force moves negative charges to one side, they cannot build up without limit. The electric field caused by their separation opposes the magnetic force, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-65b0eb6ac7cd5d21b334b64a48b0acbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#113;&#118;&#66;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"67\" style=\"vertical-align: -3px;\" \/>, and the electric force, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4129a059d5bfe1bea5a9898b08d5cfd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#70;&#125;&#95;&#123;&#101;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#113;&#69;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"63\" style=\"vertical-align: -3px;\" \/>, eventually grows to equal it. That is,<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7e97bad04313a78230cd335364846b7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#113;&#69;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#113;&#118;&#66;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: -3px;\" \/><\/div>\n<p id=\"import-auto-id1751324\">or<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ad194053755624263e2b41e8e396759c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#118;&#66;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" style=\"vertical-align: 0px;\" \/><\/div>\n<p id=\"import-auto-id1565037\">Note that the electric field <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-764e1c770271f92700e1a4fbce46c668_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> is uniform across the conductor because the magnetic field <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> is uniform, as is the conductor. For a uniform electric field, the relationship between electric field and voltage is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bef9c7b3c8359de1b8da81c80f2edede_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;&#61;&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;&#47;&#108;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -5px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-502276c66966e5a861539c7de60c26c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#108;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"5\" style=\"vertical-align: 0px;\" \/> is the width of the conductor and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/> is the Hall emf. Entering this into the last expression gives<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ae3882263cddcabb11194852385b7e4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;&#125;&#123;&#108;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#118;&#66;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/div>\n<p id=\"import-auto-id2096508\">Solving this for the Hall emf yields<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0692fee2addab2eb0b35de157658c40e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#108;&#118;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#66;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#118;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#108;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#117;&#116;&#117;&#97;&#108;&#108;&#121;&#32;&#112;&#101;&#114;&#112;&#101;&#110;&#100;&#105;&#99;&#117;&#108;&#97;&#114;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"366\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"import-auto-id1699325\">where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/> is the Hall effect voltage across a conductor of width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-502276c66966e5a861539c7de60c26c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#108;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"5\" style=\"vertical-align: 0px;\" \/> through which charges move at a speed <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef71511c70f0e4b25cc6bd69f3bc20c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id1648625\">\n<div class=\"bc-figcaption figcaption\">The Hall emf <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/> produces an electric force that balances the magnetic force on the moving charges. The magnetic force produces charge separation, which builds up until it is balanced by the electric force, an equilibrium that is quickly reached.<\/div>\n<p><span data-type=\"media\" data-alt=\"Diagram showing an electron moving to the left in a three-dimensional rectangular space with velocity v. The magnetic field is oriented out of the page. The electric field is down. The electric force on the charge is up while the magnetic force on the charge is down. An illustration of the right hand rule shows the thumb pointing to the left with v, the fingers out of the page with B, and the force on a positive charge up and away from the palm.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_23_06_02a.jpg\" data-media-type=\"image\/jpg\" alt=\"Diagram showing an electron moving to the left in a three-dimensional rectangular space with velocity v. The magnetic field is oriented out of the page. The electric field is down. The electric force on the charge is up while the magnetic force on the charge is down. An illustration of the right hand rule shows the thumb pointing to the left with v, the fingers out of the page with B, and the force on a positive charge up and away from the palm.\" width=\"300\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id1422576\">One of the most common uses of the Hall effect is in the measurement of magnetic field strength <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>. Such devices, called <em data-effect=\"italics\">Hall probes<\/em>, can be made very small, allowing fine position mapping. Hall probes can also be made very accurate, usually accomplished by careful calibration. Another application of the Hall effect is to measure fluid flow in any fluid that has free charges (most do). (See <a href=\"#import-auto-id1320873\" class=\"autogenerated-content\">(Figure)<\/a>.) A magnetic field applied perpendicular to the flow direction produces a Hall emf <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/> as shown. Note that the sign of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/> depends not on the sign of the charges, but only on the directions of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef71511c70f0e4b25cc6bd69f3bc20c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>. The magnitude of the Hall emf is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-66f999ad00dbca6e23c8b9c53c2a44cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#108;&#118;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"58\" style=\"vertical-align: 0px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-502276c66966e5a861539c7de60c26c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#108;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"5\" style=\"vertical-align: 0px;\" \/> is the pipe diameter, so that the average velocity <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef71511c70f0e4b25cc6bd69f3bc20c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> can be determined from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/> providing the other factors are known.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id1320873\">\n<div class=\"bc-figcaption figcaption\">The Hall effect can be used to measure fluid flow in any fluid having free charges, such as blood. The Hall emf <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/> is measured across the tube perpendicular to the applied magnetic field and is proportional to the average velocity <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef71511c70f0e4b25cc6bd69f3bc20c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1542617\" data-alt=\"Diagram showing a tube with diameter l with one end between the north and south poles of a magnet. The charges are moving with velocity v within the tube and out of the page. The magnetic field B is oriented across the tube, from the north to the south pole of the magnet. The force on the charges is up for positive charges and down for negative charges. e m f = B l v.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_23_06_03a.jpg\" data-media-type=\"image\/jpg\" alt=\"Diagram showing a tube with diameter l with one end between the north and south poles of a magnet. The charges are moving with velocity v within the tube and out of the page. The magnetic field B is oriented across the tube, from the north to the south pole of the magnet. The force on the charges is up for positive charges and down for negative charges. e m f = B l v.\" width=\"350\" \/><\/span><\/p>\n<\/div>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id2241844\">\n<div data-type=\"title\" class=\"title\">Calculating the Hall emf: Hall Effect for Blood Flow<\/div>\n<p id=\"import-auto-id1452723\">A Hall effect flow probe is placed on an artery, applying a 0.100-T magnetic field across it, in a setup similar to that in <a href=\"#import-auto-id1320873\" class=\"autogenerated-content\">(Figure)<\/a>. What is the Hall emf, given the vessel\u2019s inside diameter is 4.00 mm and the average blood velocity is 20.0 cm\/s?<\/p>\n<p id=\"import-auto-id2812308\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id1616771\">Because <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef71511c70f0e4b25cc6bd69f3bc20c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-502276c66966e5a861539c7de60c26c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#108;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"5\" style=\"vertical-align: 0px;\" \/> are mutually perpendicular, the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-66f999ad00dbca6e23c8b9c53c2a44cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#108;&#118;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"58\" style=\"vertical-align: 0px;\" \/> can be used to find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"import-auto-id1543446\"><strong>Solution<\/strong><\/p>\n<p id=\"import-auto-id1853017\">Entering the given values for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef71511c70f0e4b25cc6bd69f3bc20c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>, and <em data-effect=\"italics\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-502276c66966e5a861539c7de60c26c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#108;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"5\" style=\"vertical-align: 0px;\" \/><\/em> gives<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-219\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-790962957282d20d7df447ef4109706d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#108;&#108;&#125;&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;&#38;&#32;&#61;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#108;&#118;&#125;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#46;&#49;&#48;&#48;&#32;&#84;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#50;&#48;&#48;&#32;&#109;&#47;&#115;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#38;&#32;&#61;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#48;&#46;&#48;&#32;&mu;&#86;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"376\" style=\"vertical-align: -11px;\" \/><\/div>\n<p id=\"import-auto-id1484417\"><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id1465329\">This is the average voltage output. Instantaneous voltage varies with pulsating blood flow. The voltage is small in this type of measurement. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/> is particularly difficult to measure, because there are voltages associated with heart action (ECG voltages) that are on the order of millivolts. In practice, this difficulty is overcome by applying an AC magnetic field, so that the Hall emf is AC with the same frequency. An amplifier can be very selective in picking out only the appropriate frequency, eliminating signals and noise at other frequencies.<\/p>\n<\/div>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id2093608\">\n<h1 data-type=\"title\">Section Summary<\/h1>\n<ul>\n<li>The Hall effect is the creation of voltage <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-edf055e353a9fc5853e93bdaa0377d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"7\" style=\"vertical-align: 0px;\" \/>, known as the Hall emf, across a current-carrying conductor by a magnetic field. <\/li>\n<li>The Hall emf is given by\n<div data-type=\"equation\" class=\"equation\" id=\"eip-id2017144\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9d6114d94c731e13faaaa9dff0045e2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#108;&#118;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#66;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#118;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#108;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#117;&#116;&#117;&#97;&#108;&#108;&#121;&#32;&#112;&#101;&#114;&#112;&#101;&#110;&#100;&#105;&#99;&#117;&#108;&#97;&#114;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"358\" style=\"vertical-align: -4px;\" \/><\/div>\n<p>for a conductor of width <em data-effect=\"italics\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-502276c66966e5a861539c7de60c26c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#108;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"5\" style=\"vertical-align: 0px;\" \/><\/em> through which charges move at a speed <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ef71511c70f0e4b25cc6bd69f3bc20c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id1523583\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1564685\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2098332\">\n<p id=\"import-auto-id1616406\">Discuss how the Hall effect could be used to obtain information on free charge density in a conductor. (Hint: Consider how drift velocity and current are related.)<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" id=\"fs-id1544499\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2114109\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2025369\">\n<p id=\"import-auto-id1416915\">A large water main is 2.50 m in diameter and the average water velocity is 6.00 m\/s. Find the Hall voltage produced if the pipe runs perpendicular to the Earth\u2019s <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c2f52444c7a101f25ad31dd92f903631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#53;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#45;&#84;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -1px;\" \/> field.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1399045\">\n<p id=\"import-auto-id1773192\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-01a79ee8d3e0c8bcd7135464c7ddcd30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#52;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#86;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"86\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1540519\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1907612\">\n<p id=\"import-auto-id1988652\">What Hall voltage is produced by a 0.200-T field applied across a 2.60-cm-diameter aorta when blood velocity is 60.0 cm\/s?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1527365\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1066850\">\n<p id=\"import-auto-id2025116\">(a) What is the speed of a supersonic aircraft with a 17.0-m wingspan, if it experiences a 1.60-V Hall voltage between its wing tips when in level flight over the north magnetic pole, where the Earth\u2019s field strength is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-36c811e5aa0de8335176b5be62dd781d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#48;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#53;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#63;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"93\" style=\"vertical-align: -1px;\" \/> (b) Explain why very little current flows as a result of this Hall voltage.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\">\n<p id=\"import-auto-id2229613\">(a) 1.18 \u00d7 10 <sup>3<\/sup> m\/s<\/p>\n<p id=\"import-auto-id1377755\">(b) Once established, the Hall emf pushes charges one direction and the magnetic force acts in the opposite direction resulting in no net force on the charges. Therefore, no current flows in the direction of the Hall emf. This is the same as in a current-carrying conductor\u2014current does not flow in the direction of the Hall emf.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2835315\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2295527\">\n<p id=\"import-auto-id2164253\">A nonmechanical water meter could utilize the Hall effect by applying a magnetic field across a metal pipe and measuring the Hall voltage produced. What is the average fluid velocity in a 3.00-cm-diameter pipe, if a 0.500-T field across it creates a 60.0-mV Hall voltage?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1645693\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1993134\">\n<p id=\"import-auto-id1744711\">Calculate the Hall voltage induced on a patient\u2019s heart while being scanned by an MRI unit. Approximate the conducting path on the heart wall by a wire 7.50 cm long that moves at 10.0 cm\/s perpendicular to a 1.50-T magnetic field.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1529856\">\n<p id=\"import-auto-id1747279\">11.3 mV<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id976138\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1495708\">\n<p id=\"import-auto-id1158161\">A Hall probe calibrated to read <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-817a4f99365ff8788b9e35430f5da3b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#48;&#32;&mu;&#86;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -1px;\" \/> when placed in a 2.00-T field is placed in a 0.150-T field. What is its output voltage?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1797808\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1733233\">\n<p id=\"import-auto-id2194387\">Using information in <a href=\"\/contents\/a5e2058d-3bf0-4538-9e0d-d72e24a9acfd@7#fs-id1889050\" class=\"autogenerated-content\">(Figure)<\/a>, what would the Hall voltage be if a 2.00-T field is applied across a 10-gauge copper wire (2.588 mm in diameter) carrying a 20.0-A current?\n<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1399884\">\n<p id=\"import-auto-id2080944\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6d69372b3df72cbf19cd86126a071f38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#54;&#32;&mu;&#86;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1442567\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2084601\">\n<p id=\"import-auto-id1347796\">Show that the Hall voltage across wires made of the same material, carrying identical currents, and subjected to the same magnetic field is inversely proportional to their diameters. (Hint: Consider how drift velocity depends on wire diameter.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"eip-id1890293\" data-element-type=\"problems-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"eip-id1890296\">\n<p id=\"eip-id1890298\">A patient with a pacemaker is mistakenly being scanned for an MRI image. A 10.0-cm-long section of pacemaker wire moves at a speed of 10.0 cm\/s perpendicular to the MRI unit\u2019s magnetic field and a 20.0-mV Hall voltage is induced. What is the magnetic field strength?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"eip-id1890305\">\n<p id=\"eip-id1890307\">2.00 T<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl class=\"definition\" id=\"import-auto-id1648144\">\n<dt>Hall effect<\/dt>\n<dd id=\"fs-id1981047\">the creation of voltage across a current-carrying conductor by a magnetic field<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2654894\">\n<dt>Hall emf<\/dt>\n<dd>the electromotive force created by a current-carrying conductor by a magnetic field, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-66f999ad00dbca6e23c8b9c53c2a44cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#101;&#112;&#115;&#105;&#108;&#111;&#110;&#32;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#108;&#118;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"58\" style=\"vertical-align: 0px;\" \/><\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":211,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"all-rights-reserved"},"chapter-type":[],"contributor":[],"license":[56],"class_list":["post-1250","chapter","type-chapter","status-publish","hentry","license-all-rights-reserved"],"part":1204,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/1250","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/users\/211"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/1250\/revisions"}],"predecessor-version":[{"id":1251,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/1250\/revisions\/1251"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/parts\/1204"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/1250\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/media?parent=1250"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=1250"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/contributor?post=1250"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/license?post=1250"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}