# Work done in electrostatics

## Homework Statement

A metallic sphere is placed inside a hollow spherical shell. The potential on the inner and outer spheres is 10 V and 5 V respectively. What is the potential at the center?(The spheres are concentric.)

## Homework Equations

$$V =\frac{kq}{r}$$

## The Attempt at a Solution

The obvious answer I thought of was 15 V. But the answer in my text was 10 V. I know that it would be 15 V in case of two concentric spherical shells. Does having a metallic sphere make a difference?(I don't think so because for a metallic sphere the charge resides on the surface.)

gneill
Mentor
What would happen if the potential inside the metallic sphere were different from the potential at its surface?

gracy
how did you calculate 15 V?

What would happen if the potential inside the metallic sphere were different from the potential at its surface?
Then some work would be done in bringing the charge from the surface of the metallic sphere to its center. But I don't see how that could be the case.

how did you calculate 15 V?
That's quite simple. You can just assume some quantity of charge on the spheres and then assume that the charges are concentrated at the center. That would yield the work done and the potential easily.

gneill
Mentor
Then some work would be done in bringing the charge from the surface of the metallic sphere to its center. But I don't see how that could be the case.
Would the charge carriers in the metallic sphere remain static (stationary, unmoving) if the potential varied anywhere on or in it? Isn't this a problem in electrostatics?

And I don't see the connection between your thread title and your problem statement. You haven't introduced any mechanism where work will be done, or gone through the exercise of calculating the work required to move a charge from infinity to the center. As far as I can tell you just guessed at an answer (15 V).
The obvious answer I thought of was 15 V. But the answer in my text was 10 V. I know that it would be 15 V in case of two concentric spherical shells.
How do you know this? Can you demonstrate?

Maybe you summed both the potentials.. it's okay. For a metallic sphere potential at any place is same as to the surface. But is it same for a hollow sphere? I am not sure. You may do one thing, be sure about this point first then cone to the rest part.

cnh1995
Homework Helper
Gold Member

## Homework Statement

A metallic sphere is placed inside a hollow spherical shell. The potential on the inner and outer spheres is 10 V and 5 V respectively. What is the potential at the center?(The spheres are concentric.)

## Homework Equations

$$V =\frac{kq}{r}$$

## The Attempt at a Solution

The obvious answer I thought of was 15 V. But the answer in my text was 10 V. I know that it would be 15 V in case of two concentric spherical shells. Does having a metallic sphere make a difference?(I don't think so because for a metallic sphere the charge resides on the surface.)
Can you find the equipotential part in this system?

Would the charge carriers in the metallic sphere remain static (stationary, unmoving) if the potential varied anywhere on or in it? Isn't this a problem in electrostatics?

And I don't see the connection between your thread title and your problem statement. You haven't introduced any mechanism where work will be done, or gone through the exercise of calculating the work required to move a charge from infinity to the center. As far as I can tell you just guessed at an answer (15 V).

How do you know this? Can you demonstrate?
Maybe you summed both the potentials.. it's okay. For a metallic sphere potential at any place is same as to the surface. But is it same for a hollow sphere? I am not sure. You may do one thing, be sure about this point first then cone to the rest part.
The potential is constant inside a hollow sphere.

cnh1995
Homework Helper
Gold Member
The potential is constant inside a hollow sphere.
When there is net charge present on the sphere, potential due to that charge inside that sphere is constant everywhere.

How do you know this? Can you demonstrate?
Doesn't it follow from the superposition principle?

How do you know this? Can you demonstrate?
Doesn't this follow clearly from the superposition principle?

When there is net charge present on the sphere, potential due to that charge inside that sphere is constant everywhere.
Yes. I used the fact in this case.

cnh1995
Homework Helper
Gold Member
Doesn't it follow from the superposition principle?
Consider this situation. There is a charge +q on the surface of the inner sphere and outer sphere is neutral. The potential of outer sphere is kq/r=5V. What will be the potential at the center then?

fireflies
Consider this situation. There is a charge +q on the surface of the inner sphere and outer sphere is neutral. The potential of outer sphere is kq/r=5V. What will be the potential at the center then?
$$5 + \frac{kq}{r_i}$$ ?

cnh1995
Homework Helper
Gold Member
Charge is on the surface of the inner sphere. What will be the potential at it's center then?

gneill
Mentor
Doesn't it follow from the superposition principle?
If it is properly applied, yes. But you haven't shown how you applied it to arrive at a 15 V potential inside the 10 V sphere.

Charge is on the surface of the inner sphere. What will be the potential at it's center then?
$$\frac{kq}{r}$$

If it is properly applied, yes. But you haven't shown how you applied it to arrive at a 15 V potential inside the 10 V sphere.

I simply added the potential due to the two spheres.

cnh1995
Homework Helper
Gold Member
$$\frac{kq}{r}$$

I simply added the potential due to the two spheres.
When the charge is on the surface of the sphere, potential at the surface and inside the sphere is same. The sphere is at 10V potential. Potential inside the sphere everywhere should be same. This implies E field inside the sphere is 0.

When the charge is on the surface of the sphere, potential at the surface and inside the sphere is same. The sphere is at 10V potential. Potential inside the sphere everywhere should be same. This implies E field inside the sphere is 0.
So?

cnh1995
Homework Helper
Gold Member
So?
So, the potential at the center will be equal to the potential of the inner sphere, won't it? The inner sphere is at 10V. So the potential at the center is also 10V.

So, the potential at the center will be equal to the potential of the inner sphere, won't it? The inner sphere is at 10V. So the potential at the center is also 10V.
What about the potential due to the outer sphere?

cnh1995
Homework Helper
Gold Member
What about the potential due to the outer sphere?
Outer sphere is neutral. Potential of the outer sphere is 5V "due to" the charge on the inner sphere.

Outer sphere is neutral. Potential of the outer sphere is 5V "due to" the charge on the inner sphere.
I think that's where I had gone wrong.

But consider this case : If you had two concentric spherical shells with charges q1 and q2 and radii a and b, then what would be the net potential at the center? Won't it simply be potential due to sphere 1 plus potential due to sphere 2?