Phys 200B – HW1

Due Monday 09-Jan-06 08:30AM to Orpheus Mall

1. The electric charge density inside an atomic nucleus of radius a is described by

for r < a, where r_o = 0.243 e/fm³ and a = 3.4 fm. (e = 1.6 x 10^-19 C, 1 fm = 10^-15 m).

a) Determine the total charge, Q, of this nucleus.

b) Determine the electric potential, V, for an arbitrary point along the z axis.

c) Demonstrate that the maximum electric field can be found at r = 0.745 a.

2. Two concentric, spherical, conducting shells of radii a and b are maintained at potentials V_a and V_b. The region between the shells is filled with a dielectric material with dielectric constant e_r

a) What is the stored energy?

b) What is the capacitance?

3. Consider a long solenoid with a soft iron core (permeability m >> m₀).

a) What is the energy density with and without the core?

b) If the core were to be partially removed, how strong would be the force pulling the core back into the solenoid? (neglect the fringe fields)

4. If magnetic monopoles exist, then Maxwell's equations would require two additional terms to take into account the magnetic charge density (r_m) and the magnetic current density (J_m). Maxwell's equations would then read:

a) Show that (magnetic continuity equation).

b) What is the magnetic field in the near a point magnetic charge Q_m?

c) Magnetic monopoles go through a loop of copper wire. Show that the induced electromotive force is equal to minus the magnetic current (this is one method of detecting magnetic monopoles).