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(PHYS223)PHYS223F.pdf
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Final Examination of Phys 223 (May 24, 12:30-3:30 pm)
1.
A perfect dipole p is situated a distance z above an infinite grounded conducting plane. The dipole makes an angle with the perpendicular to the plane. Find the torque on p. If the dipole is free to rotate, in what direction will it come to rest? (20 points)

2.
A copper sphere, radius a, is surrounded by a concentric copper spherical shell of inner radius c (See Figure). The space between is partially filled (from b out to c) with material of dielectric constant r, as shown. Find i) the displacement vector D and the electric field E in all the regions when a potential difference V is applied between the two conductors; ii) all the bound charges b and b. iii) the capacitance of the structure. (20 points)

3.
An infinitely long circular cylinder carries a uniform magnetization M=ks2. , where k is a constant, s is the distance from the axis, and . is the usual azimuthal unit vector.

(a)
What are the bound currents?

(b)
Find the magnetic field due to M, for points
inside and outside the cylinder. (20 points)




4.
A large parallel-plate capacitor with uniform surface charge on the upper plate and C on the lower is moving with a constant speed v, as shown below.

(a)
Find the magnetic field between the plates and also above and below them.

(b)
Find the magnetic force per unit area on the upper plate, including its direction.

(c)
At what speed v would the magnetic force balance the electric force?



5.
Boundary conditions: (20 points)






(a) At the interface between one linear dielectric and another the electric
field lines bend (see Figure (a)). Show that
tan / tan = /

2 121
assuming there is no free charge at the boundary.
(b) At the interface between one linear magnetic material and another the
magnetic field lines bend (see Figure (b)). Shown that tan / tan = /
2 121
assuming there is no free current at the boundary.

(a) (b)