Problem 1:

A hollow ball of radius R has a surface charge distribution which produces a potential on the surface of V(R,q) = k(cos²q + 1), where k is a constant and q is the usual polar angle relative to the z-axis.
(a)  Find the potential at all points in space.
(b)  Show that the charge distribution on the ball is s(R,q) = (ke₀/R)(5cos²q - 1/3).

Problem 2:

An infinitely long solenoid is wound with one layer of very fine wire.  The solenoid has a radius r meters, has n turns per meter of length, and carries a current I.
(a)  What is the magnetic field inside the solenoid?
(b)  What is the magnitude of force on a short length dl of wire in a turn, and what is its direction?
(c)  What is the tension in the wire?

Problem 3:

A permanent magnet has circular pole pieces of radius a separated by an arbitrary distance.  The magnetic field B is uniform between the pole pieces.  Calculate the force between the pole pieces in terms of B and a.

Problem 4:

Find the magnetic vector potential for the case of a long, straight wire carrying a steady current I.  Let R be the radius of the wire.

Problem 5:

In Bohr's 1913 model of the hydrogen atom, the electron is in a circular orbit of radius 5.29´10^-11 m and its speed is 2.19´10⁶ m/s.

(a)  What is the magnitude of the magnetic moment due to the electron's motion?
(b)  If the electron orbits counterclockwise in a horizontal circle, what is the direction of this magnetic moment vector?

Problem 6:

A sphere of linear magnetic material is placed in an originally uniform magnetic field magnetic field B₀.  Find the new field inside the sphere.

Problem 7:

An infinitely long cylinder of radius R carries a "frozen in" magnetization parallel to the axis, M = kr, where k is constant and r is the distance from the axis.  Find B and H inside and outside the cylinder.