P25_063.PDF

63. We imagine moving all the charges on the surface of the sphere to the center of the the sphere. Using

Gauss’ law, we see that this would not change the electric ﬁeld outside the sphere. The magnitude of

the electric ﬁeld E of the uniformly charged sphere as a function of r , the distance from the center of

thesphere,isthusgivenby E ( r )= q/ (4 πε 0 r 2 )for r>R .Here R is the radius of the sphere. Thus, the

potential V at the surface of the sphere (where r = R )isgivenby

V ( R )= V r = ∞

8 . 99

+ ∞

E ( r ) dr = R

∞

1 . 50

10 8 C

4 πε 0 r 2 dr =

4 πε 0 R

10 9 N · m 2

C 2

=8 . 43

10 2 V .

0 . 160 m