# Potential of ring with sphere inside it

1. Jun 13, 2013

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

I'm trying to find the potential of conducting grounded sphere with radius Rs which located in the center of charged ring with Rr (>Rs) with charge density λ, h meters up to the z axis (see the attached images)

Rs=4.3[cm]
Rr=6.6[cm]
h=13.1[cm]
λ=1.0[esu/cm]

2. The attempt at a solution

The sphere potential is easy one -
$\Phi ring=\frac{2\pi Rr\lambda}{\sqrt{z^2+Rr^2}}$
But how do I get the potential of the sphere?
I've tried to use the image charged method, but I can't get to the right answer.
Can somebody help me?

Thanks,

#### Attached Files:

• ###### temp.jpg
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Last edited: Jun 13, 2013
2. Jun 13, 2013

### haruspex

Doesn't sound too hard . Am I missing something?

3. Jun 13, 2013

Can you give me some clue about the calculation of the sphere's potential?

4. Jun 13, 2013

### Saitama

I don't know how to calculate the sphere's potential but the problem can be easily done by method of image charges. Did you try that?

5. Jun 13, 2013

Yes.

I know how to replace a grounded sphere near to a single particle, but don't know how to replace a grounded sphere with surrounded ring.
I have only the ring’s potential on the Z axis, and it makes it harder.

6. Jun 13, 2013

### Saitama

Like a point charge, you can replace the grounded sphere with a ring here in this case.

7. Jun 13, 2013

Do you mean $\displaystyle q'=-\frac{R_s}{R_r}Q$ where $Q=\lambda \cdot 2\pi R_r$?