# Potential in case of concentric shells program

1. Nov 11, 2015

### gracy

1. The problem statement, all variables and given/known data
Three concentric spherical metallic shells A , B and C of radii a , b and c (a<b<c)have charge densities σ,−σandσ respectively . If the shells A and C are at the same potential then the relation between a , b and c is

2. Relevant equations
$V$=$\frac{Q}{4πε0r}$

3. The attempt at a solution
I know the solution

but I want to know what does it mean potential of shell A or potential of shell B,I mean what value I shall put in place of r in the formula
$V$=$\frac{Q}{4πε0r}$ for shell A,B and C?
Does potential of shell A or potential of shell B etc mean potential at the surface of shell A ,B respectively ?

Last edited: Nov 11, 2015
2. Nov 11, 2015

### BvU

Yes.
You mislead yourself by coloring in the volume of A and the volume between B and C.

There is no formula $V = \frac{1}{4πε_0r}$; typo ?

But the r in $V = \frac{Q}{4πε_0r}$ is a for A, b for B and c for C .

And the potential at a position $\vec r$ is the energy per Coulomb it takes to move a test charge from infinity (Where V = 0) to the position $\vec r$

3. Nov 11, 2015

### gracy

4. Nov 11, 2015

### BvU

Yes
Note that you can't use this for A due to the presence of B and C, nor for B due to the presence of C.
You see that in the solution at the first $\therefore$

I've always wanted to use that symbol $\therefore$ ! this is the first time

Last edited: Nov 11, 2015
5. Nov 11, 2015

### SammyS

Staff Emeritus
Yes.

In electrostatics, the potential of a conductor is uniform throughout the conductor.

6. Nov 12, 2015

### gracy

Did you mean potential of a conductor is same anywhere inside the conductor as well as on the surface of the conductor?

7. Nov 12, 2015

### SammyS

Staff Emeritus
Everywhere in the conducting material itself, as well as on the surfaces.

8. Nov 12, 2015

### BvU

Easy to remember: a conductor conducts. If there would be a potential difference, charge would be conducted until there's no more potential difference.