Total Charge (Spheres and Potential)

[jrc5135]

Homework Statement

A conducting sphere of radius a, at potential V0, is surrounded by a thin concentric spherical shell of radius b over which someone has glued a surface charge. sigma = kcos(theta) where k is a constant

i know V(r, theta) and induced surface charge on the conductor

Homework Equations

Q = integral (sigma) da

The Attempt at a Solution

trying to use equation 1 but I'm not sure first off the limits on r for each

 

[gabbagabbahey]

da is the infinitesimal area element of the surface...the entire surface is at r=b...what is your expression for da?

 

[jrc5135]

but what about the charge coming from the inner sphere at Vo my da is going to rdrdtheta

 

[gabbagabbahey]

why is there a dr term in your da, isn't r constant over a spherical surface?

Are you trying to compute the total charge on the outer shell, or the conductor, or both?

 

[jrc5135]

trying to find the charge for both

 

[gabbagabbahey]

Well, you'll have to compute the charge of each individually and then add them up.