What is the Electric Potential at a Point on the Surface of a Charged Sphere?

[utkarshakash]

Homework Statement

A point charge q is placed at a distance 2r from the centre O of a conducting charged sphere of radius r. Due to the induced charges on the sphere, find the electric potential at point P on the surface of sphere(it is at a distance 3r from q) (if Kq/r = 18 volt)

Homework Equations

The Attempt at a Solution

Due to the induced charges the potential will be 0 as there are as many -ve charge on the surface of sphere as that of +ve charge. So the net potential is due to q which comes out to be 6 but correct answer is 3.

 

[rude man]

This is best handled by image methods. Given the location of q outside your sphere, where and what size& polarity is the image charge inside the sphere? Then you dump the sphere and work with just the two point charges.

 

[utkarshakash]

This is best handled by image methods. Given the location of q outside your sphere, where and what size& polarity is the image charge inside the sphere? Then you dump the sphere and work with just the two point charges.

How can there be a net charge on the sphere when it is initially neutral? It must be zero. Half of the sphere will contain -ve charge and the other half, +ve charge.
Also what do you mean by image methods?

 

[rude man]

As I said, once the image charge is in place the sphere is gone. So there is no charged sphere or any other kind.

The function of the image charge is to geneate a field that is indistinguishable from the charge-redistributed sphere at the point of observation. The so-synthesized field is invalid for regions inside the sphere since the field inside a pure conductor has to be zero.

 

[utkarshakash]

As I said, once the image charge is in place the sphere is gone. So there is no charged sphere or any other kind.

The function of the image charge is to geneate a field that is indistinguishable from the charge-redistributed sphere at the point of observation. The so-synthesized field is invalid for regions inside the sphere since the field inside a pure conductor has to be zero.

I don't think that this simple problem requires me to use such kind of methods.

 

[consciousness]

The Attempt at a Solution

Due to the induced charges the potential will be 0 as there are as many -ve charge on the surface of sphere as that of +ve charge. So the net potential is due to q which comes out to be 6 but correct answer is 3.

The number of charges are same but they aren't uniformly distributed due to polarization. They will produce a potential.