Home Work Set # 5, Physics 217, Due: October 10, 2001

Two spherical cavities, of radii a and b, are hollowed from the interior of a neutral conducting sphere of radius R (see Figure 1). At the center of each cavity a point charge is placed; call these charges q_a and q_b.

a) Find the surface charge densities σ_a, σ_b and σ_R.
b) What is the field outside the conductor?
c) What is the field within each cavity?
d) What is the force on q_a and q_b?
e) Which of these answers would change if a third charge, q_c, were brought near the conductor?

A metal sphere of radius R carries a total charge Q. What is the force of repulsion between the "northern" and the "southern" hemisphere.

Find the capacitance per unit length of two coaxial metal cylindrical tubes, of radii a and b (see Figure 2).