Electrodynamics (II): Homework 1
Due: March 19, 2015
Exercises in Griffiths
8.2, 8.3 (hand-in 10%), 8.7 (hand-in 10%), 8.10(a)(b) (hand-in 10%), 8.14, 8.16, 8.17, 8.19
(hand-in 10%), 8.20, 8.21 (hand-in 10%)
Ex.1 10% hand-in
Consider two spherical metal shells of radii a and b. Suppose that there is a magentic dipole
of moment m
~ in the center of inner sphere. There is also a charge q on the inner sphere and
−qon the outer sphere. Find the angular momentum associated with the electromagnetic
field of the system.
Ex.2 20 % hand-in
(a) In the circuit shown in below, the capacitor has circular plates of radius r0 separated by
a distance d. Suppose that d r0 and fringing fields can be neglected. Between the plates,
it is vacuum. If at t = 0, there is a charge Q0 on the capacitor and the switch is closed.
In the quasi-static approximation, find the total electromagnetic energy that flows out from
the capacitor for 0 ≤ t < ∞. Check if the electromagnetic energy is conserved, why?
(b) A circuit of radius a in the xy plane, centered on the origin. A battery of emf V is
connected to the circuit and located at (x, y, z) = (−a, 0, 0). The battery is oriented so that
the current in the circuit flows clockwisely. If the resistance of the circuit is R, esitmate
the electromagnetic momentum of the circuit. Does the result agree with the momentum
conservation in Newtonian mechanics?
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