8.
(a) The potential as a function of r is
V (r) = V (0)
−
r
0
E(r) dr = 0
−
r
0
qr
4πε
0
R
3
dr =
−
qr
2
8πε
0
R
3
.
(b) ∆V = V (0)
− V (R) = q/8πε
0
R.
(c) Since ∆V = V (0)
− V (R) > 0, the potential at the center of the sphere is higher.
8.
(a) The potential as a function of r is
V (r) = V (0)
−
r
0
E(r) dr = 0
−
r
0
qr
4πε
0
R
3
dr =
−
qr
2
8πε
0
R
3
.
(b) ∆V = V (0)
− V (R) = q/8πε
0
R.
(c) Since ∆V = V (0)
− V (R) > 0, the potential at the center of the sphere is higher.