# Gauss' Law

1. Sep 13, 2005

I need help with this question. I can't see the motion. I have

Consider a solid sphere of radius R with a charge Q distributed uniformly. Suppose that a point charge 'q' of mass 'm', with a sign opposite that of Q, is free to move within the solid sphere. Charge q is placed at rest on the surface of the solid sphere and released. Describe the subsequent motion. In particular, what is the period of the motion, and what is the total energy of the point charge?

HELP!

2. Sep 14, 2005

### balakrishnan_v

If the charge is free to move through the sphere,the motion will be a simple harmonic one
with time period=T where T is given by
$$T=2 \pi \sqrt{\frac{4 \pi \epsilon_0 R^3 m}{Qq}}$$

3. Sep 14, 2005

### Galileo

Assume the charge will not disturb the charge density of the sphere. Use Gauss' Law to find the electric field inside the sphere. I think it's obvious what your Gaussian surface should be.
After you've found the electric field as a function of position (or distance from the sphere), you can simply calculate the force acting on the charge and use Newton's Laws to find its motion.

4. Sep 14, 2005

### balakrishnan_v

Energy of point charge is given by E where E is given by the expression that is written below
$$E=-\frac{Qq}{4 \pi \epsilon_0 R}$$