Electrodynamics (I): Homework 11
Due: January 6, 2015
Exercises in Griffiths
7.7, 7.11, 7.16, 7.18, 7.19, 7.22, 7.26, 7.27, 7.29, 7.31, 7.32, 7.33 (hand-in 5%), 7.37(hand-in
5%), 7.39, 7.44, 7.51 (hand-in 10%), 7.52, 7.58(hand-in 10%), 7.62
Ex.1 hand-in 15%
A parallel-plate capacitor is made of thin circular plate of radius a. The separation of the
plates is d and the voltage across the plate is V0 cos ωt at time t. Assuming that d a c/ω,
so that fringing of the electric field and retardation effects can be ignored.
(a) Find the electric field and magnetic fields inside the plates.
(b) If the voltage of plates is supplied by injecting or extracting current through conducting
wires connecting perpendicular to the plates at the center, find the current in the wire and
current density in the plates as a function of time.
(c) Find the magnetic field outside the plate. Check the consistency of the magnetic fields
found here and in (a) with the current density found in (b).
Ex.2 hand-in 10%
A magnetic dipole is moved from infinitely far away to a point on the axis of a conducting
loop. The magnitude of the dipole is m and the conducting loop is a perfect conductor with
self-inductance being L and radius being R. Suppose that initially the current in the loop
in zero when the dipole is far away and in the final position, the dipole points in the axial
direction of the loop and is at distance d from the center of the loop. Find the current in
the loop when the magnetic dipole is in its final position. What is the force between the
dipole and the loop?
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