# Distances where electrostatic potential is zero

1. Jun 23, 2017

### Sunbodi

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

A particle carrying charge +q is placed at the center of a thick-walled conducting shell that has inner radius R and outer radius 2R and carries charge −3q. A thin-walled conducting shell of radius 5R carries charge +3q and is concentric with the thick-walled shell. Define V = 0 at infinity.

Part A
Calculate all distances from the particle at which the electrostatic potential is zero.
Check all that apply.

Check all that apply.
r=10/3R
r=11/5R
r=5/6R
r=5/7R

2. Relevant equations

V=kQ/r

3. The attempt at a solution

0 = 1Q/R - 3Q/2R + 3Q/5R

0 = Q/10R

1/10th R is not in any of the solutions. I wonder what I'm doing wrong?

2. Jun 23, 2017

### TSny

On the right side of this equation you have several terms.

Let's take the first term: 1Q/R.

How would you describe in words what this term represents?

3. Jun 24, 2017

### Sunbodi

I miswrote it, it should be 1kQ/R but I don't think the k constant matters as much. 1kQ/R to me just means 1 volt.

4. Jun 24, 2017

### TSny

OK, I wasn't worried about the factor of k. But, can you explain why you wrote this term 1kQ/R? What does it represent?

5. Jun 24, 2017

### Sunbodi

It's the charge of the particle on the inner radius of the thick conducting shell. That's what I thought at least.

6. Jun 24, 2017

### TSny

Q is a charge. But kQ/R does not represent a charge.

Also, I'm not quite sure what you mean by "the particle on the inner radius of the thick conducting shell". The inner surface of the shell has a certain amount of charge that is uniformly spread out over the inner surface of the shell. This charge on the inner surface is "induced" by the point charge +q located at the geometric center of the shell. Can you state how much total charge is induced on the inner surface of the thick shell?

7. Jun 24, 2017

### Sunbodi

Wouldn't the charge induced simply be +Q? Sorry, I mistyped again. I meant 1kQ/R is the voltage induced on the inner radius of the thick conducting shell by the point charge.

8. Jun 24, 2017

### TSny

No. Why would you expect the induced charge on the inner surface to be positive?

If Q represents the charge of the point charge at the center, then you are right that kQ/R would be the potential at the inner surface of the thick shell due to the point charge. But I don't see how this is relevant to the question. You are trying to find points in space where the total potential (due to the point charge as well as the charges on the shells) is equal to zero.

9. Jun 24, 2017

### Sunbodi

I'm not quite sure how to set up this equation. If the total potential is zero then the sum of the potentials should be zero. This would mean the potential of charge Q at a certain point, -3Q at that point and +3Q would equal zero at this/these point(s). The charges are known, the total potential is known, the radius is not known.

Vtotal = 0 = kQ/R (point charge) + kQ/R (thick shell) + kQ/R (thin shell)

10. Jun 24, 2017

### TSny

Suppose that point P is located where the total electric potential of the system is zero. Let r be the distance of point P from the point charge +q (which is located at the center of the shells). r is the unknown that you wish to find. You will need to set up an equation that involves r and then solve the equation for r.

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