Electric Potential: Two Spherical Shells

[Bryon]

Homework Statement

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.

Homework Equations

V_b - V_a = ∫E∙dl = kQ(1/b - 1/a)

The Attempt at a Solution

V_a4 - V<sup>inf[/SUB] = -202275V OK
V_a3 - Va4 = 0V OK
V_a2 - Va3 = -77057.14286V OK
V_a1 - Va2 = 0V OK
V(0.15) - V_a1 = -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?</sup>

 

[SammyS]

-237933.333V + 1.4x10⁵ V = V(0.15) - V_a1 + V_∞, which isn't what you want.

It appears to me that what's being asked for is V(0.15) ‒ V_∞ .

You need (V(0.15) ‒ V_a1) + (V_a1 ‒ V_a2) + (V_a2 ‒ V_a3) + (V_a3 ‒ V_a4) + (V_a4 ‒ V_∞).

I believe that your first answer, V_a4 - V^{inf[/sub] = -202275V, assumed that the potential at infinity was unspecified, so you used zero.}