Electrodynamics (I): Homework 5
Due: Noverber 6, 2014
Exercises in Griffiths
3.22, 3.23(hand-in 10%), 3.24, 3.25(hand in 10%), 3.28(hand-in 5%), 3.29, 3.43, (hand-in
15%), 3.44, 3.52(a-c) (hand-in 15%)
Ex.1 hand-in
Solving the Lapace equation in spherical coordinates allows one to deal with capacitors
whose configurations are not perfectly symmetric. An example is the capactor made by
two concentric spherical metal shells. In real situation, it may occur that the two spherical
metal shells are not perfectly concentric as shown in Fig. 1. Suppose that radii of two
metal shells are b and a with b < a. Their centers are displaced by a small amount η along
z-axis. Take the center of the sphere b as the origin.
a
η
b
FIG. 1: Schematic plot of a non-parallel plate capacitor
(a) 5% Show that to O(η), the equation of the surface of sphere a is r = a + ηP1 (cos θ),
where θ is the polar angle in spherical coordinate.
(b) 10% Suppose that sphere b is grounded and the potential of sphere a is V . Find the
potential V (r, θ) between two metal shells to O(η). From V (r, θ), find the capacitance of
this system to O(η).
1