# Electromag problem

1. Nov 20, 2007

### magicuniverse

The problem statement, all variables and given/known data

1, What is the electric field around the conducting sphere of radius R carrying a charge Q?
2, What is the electric potential at the surface of the sphere if the potential infinately far away is zero?
3, Hence obtain a formula for the capacitance of the sphere.
4, Assuming the Earth to be a huge conducting sphere of radius 6.4*10^4 m surrounded by air find the capacitance of the earth.

The attempt at a solution

I have a solution for 1 which is E=kQ/r^2. I cannot do the rest of it, although i beleive that I have to use gausses law although i quite simply dont know how to do this. Any helps or suggestions would be more that welcome.

Many Thanks.

2. Nov 22, 2007

### learningphysics

V(R) - V(infinity) = $$-\int_{\infty}^{R}\vec{E}(r)\cdot\vec{dr}$$

This is just the definition of electric potential.

V(infinity) = 0, so:

V(R) = $$-\int_{\infty}^{R}\vec{E}(r)\cdot\vec{dr}$$

Use your formula for E(r) from part a). Solve the integral.