# Simple doubt in induced charge

1. Aug 2, 2013

### Vibhor

When a positive point charge q is brought close to a neutral conducting spherical shell then negative charges will be induced on the part of the shell closer to q and equal positive charges will appear on side of the shell farther from q.I understand this part.

But if the conducting spherical shell contains a charge +Q,then,if charge q is brought close to the shell ,what will happen ?

There are two possibilities

1) Fewer positive charges will be present on the side of shell near the charge q ,say Q1 ,and higher concentration of charges,say Q2, on the side of shell farther from q ,such that Q1+Q2=Q

2) Negative charges will be induced ,say -Q1,on side of the shell close to q and positive charge,Q1+Q will be present on the side farther from q.

I am not sure which of the possibilities is correct.

2. Aug 2, 2013

### Staff: Mentor

It depends on the magnitude of q relative to Q. If q is very small, you get your situation #1. If q is very large, you get your situation #2.

3. Aug 2, 2013

### Abhilash H N

You have brought a charge +q near a charged conductor having charge +Q right? When then get closer to each other there will one force acting known as coulumb force. So the chagres might repel each other.
So when you bring them togather you have to do work.
Other things go on as jtbell suggested.

4. Aug 3, 2013

### Vibhor

Thanks jtbell :-)

And in both the cases the charges rearrange themselves such that the external electric field is cancelled within the conducting metal .Correct?

5. Aug 3, 2013

### vanhees71

Yes, the interior is field free, if there are no charges inside. The problem can be solved analytically by the use of the method of image charges. Start with the problem with zero charge on the shell. The problem with a total charge Q on the shell is then solved by simply distributing this additional charge homogeneously over the shell. This is clear from the physics of this phenomenon: If you put the charge close to the shell the conduction electrons will rearrange such that the total force on them vanishes. Now you can homogeneously distribute any amount of additional charges on the surface without changing this balance.

A complete treatment can be found in Jackson, Classical Electrodynamics