A point charge q = -8 µC is surrounded by two thick, conducting spherical shells of inner and outer radii a1 = 0.3 m, a2 = 0.4 m, a3 = 0.7 m, and a4 = 0.8 m respectively. The inner shell is uncharged; the outer shell has a net charge Q = -10 µC. At this point in the problem, the potential at infinity is unspecified.
Vb - Va = ∫E∙dl = kQ(1/b - 1/a)
The Attempt at a Solution
Va4 - Vinf[/SUB] = -202275V OK
Va3 - Va4 = 0V OK
Va2 - Va3 = -77057.14286V OK
Va1 - Va2 = 0V OK
V(0.15) - Va1 = -239733.3333V
The final part of the problem asks this:
If now you are given V(inf) = 1.4 x 10^5 V, find the potential at r = 0.15 m.
I tried to do it like this:
-237933.333V + 1.4x10^5 = -99733.3333V which is incorrect. Do I have to go and find each one with respect to v(inf) = 1.4x10^5? Or do I need to find the total charge of the outermost shell and then find the potential from there to 0.15m?