Electric potential of concentric spheres

[5te4lthX]

Homework Statement

attached image
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Homework Equations

V = integral of E * dr

The Attempt at a Solution

I do not completely understand the solution to part B. I was able to solve it with the use of hints.

My guess to the explanation is: the electric field is 0 in the hollow conducting sphere/shell and thus the potential should at the inner surface and the outer surface should be equal.

However, I do not know why the potential is kq/c and not kq/b.

Also, I do not know the solution to part C (the hint says it involves both variables a and b).

My attempt at part C was kq/a

 

[Infinitum]

Since the electric field for b<r<c is zero, charge is uniformly distributed on the outer part of the sphere. So the potential for points B and C(and anything in between) should be...?

Edit: I thought this would be a better way to solve. Do you know Shell Theorem? What does that imply on the potential inside the sphere?

 

[Saitama]

Since E=-dV/dr, and E inside the sphere is zero, therefore -dV/dr is zero and therefore V=constant as the rate of change of potential is zero. Hence, the potential inside the sphere is equal to the potential at the surface of sphere.

 

[ehild]

Homework Equations

V = integral of E * dr

You missed a minus sign, and do not forget that the integration involves an additional constant.
If E=kq/r² the potential is

V=-\int{Edr}=-\int{k\frac{q}{r^2}}=k\frac{q}{r}+C

It is very important to note that the potential is continuous. It does not jump at an interface. You need two find the constant C for each domain.

The potential is zero at infinity. That means C=0 for r≥c, V=kq/r for r≥c,so it is V(c)=kq/c at the outer surface of the hollow sphere.

The electric field is zero inside a conductor so the potential is constant.
The potential is continuous, it is the same at the inner side of the outer surface as outside: V=kq/c, and stays the same in the whole shell, even at radius b: V(b)=kq/c.

The potential in the empty space between r=a and r=b is of the form V(r)=kq/r+C' again, with a different constant as in the domain r>c. And the continuity requires that V(b)=kq/b+C'=kq/c at r=b. Find C', and then calculate V(a).

ehild