1. A thin sheet of sides 2a and 2b lying in the xy plane and centeredat the origin has a uniform charge density o (see figure).a. Using the result of Example 1 in the Chapter 23 slides, showthat the electric field on the z-axis is given byofabE = 4k,o arctan |zva² + b² + z².To get full credit you must show an appropriate differentialof charge dq and explain any symmetry arguments youmight have use to arrive to this result.b. What is the field in the limit a and b going to infinity?Compare your answer with the result of the What If? in Example 3 in the Chapter 23 slides.c. Using the results of part (a), find an integral expression for the electric field at an arbitrarypoint on the x-axis created by a cube of side 2a centered at the origin with uniform volumecharge density p. You do not need to solve this integral.

a) Divide the sheet into two sections. The transverse component of the energy element cancel out,…

To get full credit you must show an appropriate differential of charge dq and explain any symmetry arguments you might have use to arrive to this result. What is the field in the limit a and b going to infinity? Compare your answer with the result of the What If? in Examp

To get full credit you must show an appropriate differential of charge dq and explain any symmetry arguments you might have use to arrive to this result. What is the field in the limit a and b going to infinity? Compare your answer with the result of the What If? in Examp

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter24: Gauss’s Law

Section: Chapter Questions

Problem 24.10P: The electric field everywhere on the surface of a thin, spherical shell of radius 0.750 m is of...

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Concept explainers

Ising model of Ferromagnets

The Ising model is one of the easiest and most famous theoretical models for ferromagnetism in statistical mechanics. When a group of atomic spins aligns such that their magnetic moments are pointed in the same direction and produce a strong permanent magnetic moment in macroscopic size, the phenomenon is called ferromagnetism. The relative permeability of these magnets is greater than unity and increasing magnetization with the applied external field. Even in the absence of an external magnetic field, these substances retain spontaneous magnetization. An example of ferromagnets is iron.

Question

1. A thin sheet of sides 2a and 2b lying in the xy plane and centered
at the origin has a uniform charge density o (see figure).
a. Using the result of Example 1 in the Chapter 23 slides, show
that the electric field on the z-axis is given by
of
ab
E = 4k,o arctan |
zva² + b² + z².
To get full credit you must show an appropriate differential
of charge dq and explain any symmetry arguments you
might have use to arrive to this result.
b. What is the field in the limit a and b going to infinity?
Compare your answer with the result of the What If? in Example 3 in the Chapter 23 slides.
c. Using the results of part (a), find an integral expression for the electric field at an arbitrary
point on the x-axis created by a cube of side 2a centered at the origin with uniform volume
charge density p. You do not need to solve this integral.

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