# Homework Help: Electric field outside conductor if charge placed inside it

1. May 4, 2012

### jd12345

1. The problem statement, all variables and given/known data
A conductor with inner radius R and outer radius 2R. A charge q is kept at a distance d<R but it is not at the centre. What will be the electric field outside the conductor? Will the charge distribution be uniform?

2. Relevant equations

3. The attempt at a solution
i suppose charge distribution will not be uniform as q is not at the centre(but im not sure)
electric field outside the conductor will be only due to q right? Or will it be zero (im confused)

2. May 4, 2012

### SammyS

Staff Emeritus
I'm assuming that the conductor's outer surface is a sphere.

3. May 4, 2012

### collinsmark

This is a good problem to think about for awhile. There might also be an example within your textbook/coursework that can help you through this. So I won't give you direct hints. But I will give the following guidance:

There are two charge distributions to consider. There is the charge distribution on the inside surface of the shell and a different distribution on the outside surface of the shell.

You might ask, "Where do these charge distributions originate from?" The answer is basically this:
1. The static electric field within a conductor (i.e. within the conducting material itself; inside the metal itself) is always zero.
2. If a charge is brought near a conducting object, it will induce a surface charge distribution on the surface of the conducting object to ensure that the electric field in the conducting material itself is zero. The surface charge distribution will automatically arrange itself in whatever way it takes to ensure that that the electric field in the conductor is zero.

When considering the surface charge distribution on the interior of the shell, ask yourself, "Qualitatively speaking, what characteristics does the surface charge distribution have at r = R to force E = 0 in the region R < r < 2R?

For the charge distribution on the exterior of the shell, ask yourself the same thing, but also note that the shell itself is not charged. The net charge on the shell (including both inside and out) is zero. So if there is some charge on the inside of the shell, there must be an equal and opposite amount charge on the outside of the shell.

When considering the electric field outside the conductor, consider Gauss' Law.

[Edit: I see SammyS beat me to the response.]

4. May 4, 2012

### jd12345

Okay i am clear about the charge distribution at the interior and exterior of the conductor
But i have a doubt about the electric field outside the conductor

Gauss law states that Electric Flux = Charge enclosed / ε
Well the net charge inside is just q but you can't take out the electric field outside the integral of the electric flux because electric field is not unifrom outisde the sphere( as charge distribution on the sphere is not uniform)

5. May 5, 2012

### collinsmark

Yes,that's right.
Wait, think about this some more. Remember the electric field inside the (metal) conducting material itself is 0. What sort of charge distribution on the outside of the outer surface of the shell would be required such that the electric field is zero on the inside?

6. May 5, 2012

### jd12345

Okay got it(after lot of thinkng) - at the inner surface charge distribution will be non-uniform. At the outer surface charge distribution will be uniform to keep the electric field zero inside the conductor.
So you can take out the electric field outsidee the integral and figure out the electric field