Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Chapter 2.5, Problem 2.45P
To determine
The electric field at a height z above the center of a square sheet having side a carry a uniform surface charge density
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Students have asked these similar questions
An infinitely long cylinder in free space is concentric with the z-axis
and has radius a. The net charge density p in this cylinder is given in
cylindrical coordinates by,
1
a² +r²
where A is a constant.
(a) Show that the total charge per unit length, λ in the cylinder is
λ = πA ln 2.
p(r) = A-
Hint: you may find the following integral useful.
1
2
J
for r a) and inside the
cylinder (r< a).
(d) The cylinder is composed of a material in which the polarisation P
is given by
P = P₁² in (1 +5²) e₁₁
er,
r
where Po is a constant.
Determine the bound charge density pb in the cylinder. Hence, or
otherwise, determine a relation between A and Po such that the
free charge density of in the cylinder vanishes.
Consider an infinite sheet of charge in the xy-plane with uniform charge density Ps.
The charge associated with an elemental area ds is:
P(0, 0. A)
What would be the electric field for z0 << R and z0 >> R for the following integral? The integral is the answer to the following question:
"A uniformly charged disk with charge Q and radius R sits in the xy-plane with its center at theorigin. Take z0 to be some point on the positive z-axis. What is the electric field at z0? Leave your answer in the form of a well-defined definite integral."
Chapter 2 Solutions
Introduction to Electrodynamics
Ch. 2.1 - (a) Twelve equal charges,q, arc situated at the...Ch. 2.1 - Find the electric field (magnitude and direction)...Ch. 2.1 - Find the electric field a distance z above one end...Ch. 2.1 - Prob. 2.4PCh. 2.1 - Prob. 2.5PCh. 2.1 - Find the electric field a distance z above the...Ch. 2.1 - Find the electric field a distance z from the...Ch. 2.2 - Use your result in Prob. 2.7 to find the field...Ch. 2.2 - Prob. 2.9PCh. 2.2 - Prob. 2.10P
Ch. 2.2 - Use Gauss’s law to find the electric field inside...Ch. 2.2 - Prob. 2.12PCh. 2.2 - Prob. 2.13PCh. 2.2 - Prob. 2.14PCh. 2.2 - A thick spherical shell carries charge density...Ch. 2.2 - A long coaxial cable (Fig. 2.26) carries a uniform...Ch. 2.2 - Prob. 2.17PCh. 2.2 - Prob. 2.18PCh. 2.2 - Prob. 2.19PCh. 2.3 - One of these is an impossible electrostatic field....Ch. 2.3 - Prob. 2.21PCh. 2.3 - Find the potential a distance s from an infinitely...Ch. 2.3 - Prob. 2.23PCh. 2.3 - Prob. 2.24PCh. 2.3 - Prob. 2.25PCh. 2.3 - Prob. 2.26PCh. 2.3 - Prob. 2.27PCh. 2.3 - Prob. 2.28PCh. 2.3 - Prob. 2.29PCh. 2.3 - Prob. 2.30PCh. 2.4 - Prob. 2.31PCh. 2.4 - Prob. 2.32PCh. 2.4 - Prob. 2.33PCh. 2.4 - Find the energy stored in a uniformly charged...Ch. 2.4 - Prob. 2.35PCh. 2.4 - Prob. 2.36PCh. 2.4 - Prob. 2.37PCh. 2.5 - A metal sphere of radius R, carrying charge q, is...Ch. 2.5 - Prob. 2.39PCh. 2.5 - Prob. 2.40PCh. 2.5 - Prob. 2.41PCh. 2.5 - Prob. 2.42PCh. 2.5 - Prob. 2.43PCh. 2.5 - Prob. 2.44PCh. 2.5 - Prob. 2.45PCh. 2.5 - If the electric field in some region is given (in...Ch. 2.5 - Prob. 2.47PCh. 2.5 - Prob. 2.48PCh. 2.5 - Prob. 2.49PCh. 2.5 - Prob. 2.50PCh. 2.5 - Prob. 2.51PCh. 2.5 - Prob. 2.52PCh. 2.5 - Prob. 2.53PCh. 2.5 - Prob. 2.54PCh. 2.5 - Prob. 2.55PCh. 2.5 - Prob. 2.56PCh. 2.5 - Prob. 2.57PCh. 2.5 - Prob. 2.58PCh. 2.5 - Prob. 2.59PCh. 2.5 - Prob. 2.60PCh. 2.5 - Prob. 2.61P
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- = Let er be the unit radial vector field. Compute the outward flux of the vector field F er/r² through the ellipsoid 4x² + 6y² + 9z² = 36. [Hint: Because F is not defined at zero, you cannot use the divergence theorem on the bounded region inside of S. ]arrow_forward(a) Consider a uniformly charged, thin-walled, right circular cylindrical shell having total charge Q , radius R, and length l. Determine the electric field at a point a distance d from the right side of the cylinder as shown in the Figure. Suggestion: treat the cylinder as a collection of ring charges. (b) Consider now a solid cylinder with the same dimensions and carrying the same charge,uniformly distributed through its volume.arrow_forwardA line of charge extends from x- -a to z - 0. The rod has a uniform linear charge density A. Our goal is to determine the electric field at point P on the y axis, at an arbitrary height y above the right end of the rod. In this problem, DO NOT EVALUATE any integrals. Instead, your answers will be the integrand - i.e., the function to be ingrated. What integral should you evaluate to determine the z-component of the electric field at point P? E - /- dr What should the limits on the integral be? From to What integral should you evaluate to determine the y-component of the electric field at point P? |Ez- dr What should the limits on the integral be? From toarrow_forward
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