Electrodynamics (I): Homework 3
Due: October 23, 2014
Exercises in Griffiths
2.43 (hand-in 5%), 2.47, 2.53(30%, hand-in), 2.59, 2.60
Ex.1 hand-in 5%
Consider two conducting spheres with radii being a and b respectively. If the distance
between centers of these two conducting spheres is c and c a, b, estimate the capacitance
(in approximation) of this system.
Ex.2 hand-in
(a) 10% Calculate the potential in all space V (x, y, z) due to an infinitely long line with
charge per unit length λ at x = −b, y = 0 and another infinitely long line with charge per
unit length −λ at x = b, y = 0. Both lines are parallel to the z-axis. Take V = 0 at the
origin. Sketch the equipotential surfaces.
(b) 15% Consider two identical conducting cylinders in vacuum. Both cylinders are infinitely
long and have the same radius R = 3a. The axis of both cylinders are on the xz plane and
parallel to the z-axis, one at x = −5a, y = 0 and the other at x = 5a, y = 0. An electrical
potential difference of V0 is applied between the two cylinders with the cylinder at x = −5a
be in higher potential. If we set the potential V = 0 at the origin, using results of (a) to
find the potential in all regions. From the potential, find the capacitance (per length) of the
system.
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