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A current I flows to the right through a rectangular bar

Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths ISBN: 9780321856562 45

Solution for problem 41P Chapter 5

Introduction to Electrodynamics | 4th Edition

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Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths

Introduction to Electrodynamics | 4th Edition

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Problem 41P

Problem 41P

A current I flows to the right through a rectangular bar of conducting material, in the presence of a uniform magnetic field B pointing out of the page

(Fig. 5.56).

(a) If the moving charges are positive, in which direction are they deflected by the magnetic field? This deflection results in an accumulation of charge on the upper and lower surfaces of the bar, which in turn produces an electric force to counteract the magnetic one. Equilibrium occurs when the two exactly cancel. (This phenomenon is known as the Hall effect.)

(b) Find the resulting potential difference (the Hall voltage) between the top and bottom of the bar, in terms of B, v (the speed of the charges), and the relevant dimensions of the bar.23

(c) How would your analysis change if the moving charges were negative? [The Hall effect is the classic way of determining the sign of the mobile charge carriers in a material.]

Figure 5.56

Step-by-Step Solution:
Step 1 of 3

E=1.60*10^-19 C…. Coulombs is the unit of the charge. Mass of e is much less than protons and neutrons and that explains why electrons are so mobile. Electric forces acts on the charges, but this electric force cannot actually be seen and can explain why protons repel and electrons repel. Force is an important law in regards to point charges. Newtons 3 law of motion (action and reaction) same magnitude with opposite direction when the two point charges are opposite causing the directions to be in opposition. Magnitude is the absolute value. F is directly proportional to the magnitudes of q1 and q2 (similar to gravitational force). But now there is a constant k which is the proportionality constant. Epsilon = permittivity of free space (free space = vacuum) with specific units.

Step 2 of 3

Chapter 5, Problem 41P is Solved
Step 3 of 3

Textbook: Introduction to Electrodynamics
Edition: 4
Author: David J. Griffiths
ISBN: 9780321856562

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A current I flows to the right through a rectangular bar