Work to Construct Conducting Spheres

[Ferbs207]

1. Homework Statement

How much work does it take to construct a conducting sphere of radius 'a' and charge '+q' by pulling charges ('dq') from an infinite distance? Then construct another conducting sphere of radius 'b' and charge '-q' around the sphere of radius 'a'. Given 'a'<'b'.

2. Homework Equations
F=ke(q_1)(q_2)/r^2
E=ke(integral(dq/r^2)
U=integral(F)=1/q(integral(E))
W=delta(U)

3. The Attempt at a Solution

If the charges are initially infinitely far, then the initial potential energy is 0. This means that all I need to do is calculate the potential energy of the sphere at radius 'a', which will be my value for work. Let's say the potential energy at radius 'a' is U_a.

It's the second part of the question that I find difficult. How do I account for the interactions between the two conducting sphere when constructing the second one around it?

 

[kuruman]

Hi Ferbs207 and welcome to PF. Please follow the rules of this forum and use the template when you seek help with homework. Show us the relevant equations and tell us what you tried and what you think about the problem. We just don't give answers away.