What is the electric field between the shells?
What is the relationship between electric field and electric potential?
[Edit: Oh, and I just realized that you'll also have to calculate the electric potential is outside both shells too, since the absolute values of the charges are not equal. So what is the electric field and/or the electric potential outside of the outer shell?]
[Second edit: Thinking about this problem a little more, the problem might be a little ambiguous. I think the answer depends on which shell the charge is applied. I.e. in the C = Q/V, is the charge Q applied to shell
a with the charge on shell
b following it's own charge accordingly, or is the charge applied to shell
b with shell
a following accordingly. In other words, I think it matters how Q is defined. How does the measured charge get to the system. By what mechanism/configuration is it that Q is being measured, and thus the capacitance. Is there a wire attached to shell
a that can measure the current)and some hidden mechanism on shell
b that ensures the σ
b = -σ
a relationship, or is it the other way around (swapping
a and
b)? Or, is Q defined as the net charge on both spheres?
By all that I mean it can be looked at the following way. When you measure the capacitance of something you measure it between two terminals. Say between two wires. But the problem statement didn't specify where these wires are. Is one wire attached to each shell? And if so, is the extra change (that keeps the σ
b = -σ
a relationship) flowing in/out of shell
a or shell
b? Or is one of the wires out at infinity, similar to a single-shell, spherical capacitor? ... I'm starting not to like this problem.
]