# Charged Metallic Sphere Touching Spherical Shell From Inside

chayanne

## Homework Statement

(From Physics for Scientists and Engineers, 7E, Serway-Jewett Chapter 25 Q11)

(i) A metallic sphere A of radius 1 cm is several centimeters away from a metallic spherical shell B of radius 2 cm. Charge 450 nC is placed on A, with no charge on B or anywhere nearby. Next, the two objects are joined by a long, thin, metallic wire (as shown in Fig. 25.20), and finally the wire is removed. How is the charge shared between A and B?

(a) 0 on A, 450 nC on B
(b) 50 nC on A and 400 nC on B, with equal volume charge densities
(c) 90 nC on A and 360 nC on B, with equal surface charge densities
(d) 150 nC on A and 300 nC on B
(e) 225 nC on A and 225 nC on B
(f) 450 nC on A and 0 on B
(g) in some other predictable way
(h) in some unpredictable way

(ii) A metallic sphere A of radius 1 cm with charge 450 nC hangs on an insulating thread inside an uncharged thin metallic spherical shell B of radius 2 cm. Next, A is made temporarily to touch the inner surface of B. How is the charge then shared between them? Choose from the same possibilities. Arnold Arons, the only physics teacher yet to have his picture on the cover of Time magazine, suggested the idea for this question.

## Homework Equations

- V=kq/r (used in part (i))

Possibly relevant :
- V=k ∫dq/r,
- V=-∫E°dl,

## The Attempt at a Solution

For part (i) I was able to reach an answer using V1 = V2, assuming conservation of charge:

kq1/r1 = kq2/r2;
where q1+q2=450 nC

However for part (ii) I am pretty lost. Ideas I have tried were a similar solution to part (i), a cavity within a conductor (suggesting E inside the spherical shell should be 0), or the fact that net electric charge of a conductor is on its surface.

My attempts were unfruitful. A similar solution to (i) doesn't make all that sense to me, as I feel like they become the same thing when they touch one another (sounds romantic). Cavity within a conductor (which I literally just pulled off the textbook as I was looking for an idea to help me solve it) kind of seemed to be helpful, however, I might be misinterpreting it to make my case here. The net electric charge on surface idea also seems to lose ground when I think about the inside sphere's surface being part of the "sphere inside shell" object's surface, therefore having charge on it.

Thank you very much for your help and time.