I seriously need help on this college physics problem?

Question

small charged sphere of radius a=1.00 cm is suspended by a nylon thread inside a larger neutral, conducting sphere. The larger sphere has an interior radius b=3.10 cm and is Δ=0.5 cm thick. The charge on the small sphere is q=0.90 nC. The two spheres are concentric and insulated from their surroundings. For the following questions, the origin of our coordinates is the center of the spheres.

1) What is the magnitude of the electric field just inside the larger sphere?


2)What is the magnitude of the electric field at a radius 3.35 cm?

3) What is the magnitude of the electric field at a radius 10.0 cm?

4) What is the magnitude of the electric potential at the surface of the smaller sphere?

5) What is the magnitude of the electric potential at the outside surface of the larger sphere?



I've been trying to figure out this problem for couple of hours now, i cant seem to figure it out....please help

Answer 1

Given: r = 0.0100m at the surface of the smaller sphere;
r = 0.0310m at the interior surface of the conducting shell;
r = 0.0360m at the outer surface of the conducting shell.
Using e0 to note Epsilon_0.
According to Gause's Law: E*4*pi*r^2*e0 = q = 9x10^(-10) C:
(1) |E| = 9x10^(-10) /[4*pi*(0.0310)^2*e0] (C/m^2)
(2) r = 3.35cm is in the metal. Remember: there is no E-field in the metal, otherwise the electrons would move against the E-field, and hence finally there is still no E-field in the metal. At such static state, there is charge (-q) on the inner surface of the metal shell, and there is charge (q) on the outer surface of the metal shell. Hence in this case:
|E| = 0
(3) |E| = 9x10^(-10) /[4*pi*(0.100)^2*e0] (C/m^2)
(4) Remember E = - dV/dr in this case:
V = 9x10^(-10) /[4*pi*(0.0100)*e0] (V)
(5) V = 9x10^(-10) /[4*pi*(0.0360)*e0] (V)
Please calculate the numerical values yourself.