28_Lec-14

28_Lec-14 - Physics 241 Lecture 14 Y. E. Kim October 7,...

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Physics 241 Lecture 14 Y. E. Kim October 7, 2010 Chapter 27 Section 7 Chapter 28, Sections 1 and 2 October 7, 2010 University Physics, Chapter 26 and 27 1
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October 7, 2010 University Physics, Chapter 27 2 The Hall Effect (1) ± Consider a conductor carrying a current i perpendicular to a magnetic field B as illustrated below ± makes the electrons move toward one edge of the conductor Æ This creates and produces Æ The Hall potential is V H = Ed where d is the width of the conductor Æ When equilibrium is reached () e van t iparall l ± E , F qvBq u ± ± vB ² v dv m
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October 7, 2010 University Physics, Chapter 27 3 ± The Hall effect can be used to measure magnetic fields by applying a known current in the conductor and measuring the resulting electric field across the conductor ± Earlier we had found that the drift speed of an electron in a conductor can be related to the current density J in the strip where A = dh where h is the thickness of the conductor, and n is the number of electrons per unit volume in the conductor Æ The manetic field is given by in terms of V H , h, and n The Hall Effect (2) E B F e vB ± i v H V Ed dv m An dhn Vdhn Vhn di
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Magnetic Fields from Moving Charge (1) Biot-Savart Law 0 2 4 ȝT Y U dB ʌU u 7 0 2 N 41 0 A S P ± §· u ¨¸ ©¹ Permeability constant o Moving point charge: 0 2 4 ȝ id s r u o Bits of current: I Biot-Savart Law / T m A ² also 7KH PDJQHWLF ILHOG mFLUFXODWHVn DURXQG WKH ZLUH±
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October 7, 2010 University Physics, Chapter 28 5 ± We can write the magnetic field produced by a current element id s as ± This formula is the Biot-Savart Law ± P 0 is the magnetic permeability of free space whose value is Magnetic Fields from Moving Charge (2) 0 3 4 r dB S u 7 0 Tm 41 0 A PS ± ²
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October 7, 2010 University Physics, Chapter 28 6 Magnetic Fields from Moving Charge (3) ± The direction of the magnetic field produced by the current element is perpendicular to both the radial direction and to the current element ± The magnitude of the magnetic field is given by where T is the angle between the radial direction and the current element ± We will now calculate the magnetic field for various current element distributions 0 2 sin 4 id s dB r P S
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October 7, 2010 University Physics, Chapter 28 7 Magnetic Field from a Long, Straight Wire (1) ± First application: calculate the magnetic field from an infinitely long straight wire ± We calculate the magnetic field dB at a point P at a distance r from the wire as illustrated below ± The magnitude of the magnetic field will be given by the Biot-Savart Law and the direction will be out of the page
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October 7, 2010 University Physics, Chapter 28 8
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28_Lec-14 - Physics 241 Lecture 14 Y. E. Kim October 7,...

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