# Physics Question on Electric Field

1. May 19, 2013

### theunbeatable

1. The problem statement, all variables and given/known data

A solid conducting sphere of radius r1 has a total charge of +3Q. It is placed inside (and concentric with) a conducting spherical shell of inner radius r2 and outer radius r3. Find the electric field in these regions:
r < r1
r1 < r < r2
r2 < r < r3
r > r3

2. Relevant equations

E = F / q
E = kq / R (for a point charge)

3. The attempt at a solution

Because it's a conductor, I know that the electric field for r < r1 should be 0 (I also forgot the reasoning for this. I think it's because the charges are moving and somehow they cancel each other out?)

I'm confused on the other parts, though. For r1 < r < r2, I said that the electric field is 3kQ/r because the electric field from the sphere could be felt from that point. For r2 < r < r3, I said that the electric field was 0 for the same reasoning as r < r1, and I'm not even sure if that makes sense. Finally, for r > r3, I said it was 3kQ / r.

2. May 19, 2013

### Staff: Mentor

Careful. That formula is not quite right.

Except for that, your answers are fine. For electrostatic equilibrium, the field inside a conductor must be zero, otherwise charges would move until they canceled the field.

3. May 19, 2013

### theunbeatable

Oops, that should be R2 haha. So my answers were correct then?

And also, if both the sphere and the shell were insulators, would the answers be the opposite? Like for r < r1, the answer would be 3kQ/(r12)?

4. May 19, 2013

### Staff: Mentor

Yes, except as noted.

Not exactly. If the sphere were a uniformly charged insulator, then the field at any point within the sphere (say at r = ra, where ra < r1) would only depend on the charge within the region 0 < r < ra.

5. May 19, 2013

### barryj

Are you sure that E = kq / R (for a point charge) is correct?

6. May 19, 2013

### theunbeatable

So it would have to be 3kQ/(r2) then.

7. May 19, 2013

### Staff: Mentor

No. 3Q is the total charge of the sphere. All you want is the charge within r.

8. May 19, 2013

### theunbeatable

Since r is an arbitrary length that is less than r1, how would we determine what the charge would be?

9. May 19, 2013

### Staff: Mentor

If the sphere were uniformly charged, then the charge would be proportional to the volume.

10. May 19, 2013

### CAF123

To find the charge contained within a sphere with radius less than $r_1$, you will need to use the volume charge density of the sphere, where $dq = \rho dV$

11. May 19, 2013

### theunbeatable

That makes sense. Thanks for the help everybody!