Solve Electromagnetism Problems: Electric Field, Potential & Capacitance

[magicuniverse]

Homework Statement

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 believe that I have to use gausses law although i quite simply don't know how to do this. Any helps or suggestions would be more that welcome.

Many Thanks.

 

[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.