Potential Due to a Charged non conducting sphere

[snshusat161]

Homework Statement

$$\bold{V}\ =\ \frac{Q\,(3R^2\ -\ r^2)}{4\,\pi\,\varepsilon_0 \ \ {2R^3}}$$

Potential inside the sphere.

Homework Equations

Electric field inside the sphere (non conducting):


$$\bold{E}\ =\ \frac{Q.r}{4\,\pi\,\varepsilon_0\,R^3}$$

and

$$\bold{V}\ = \int E.dr$$

In one dimension.

The Attempt at a Solution

Even when we use both the formula's I've given we don't get the one given in the book. Does anybody here have some suggestion to find, how they have derived it.

 

[gadje]

How have you used the formulae you are given? What have you tried to do?

Note that to calculate the potential you must integrate from infinity up to the point that you're concerned about - in this case the formula for the electric field changes between infinity and your point.

 

[snshusat161]

What do you know about the electric field inside a charged sphere?

Electric field is zero inside charged conducting sphere but not in the case of non conducting sphere.

 

[gadje]

Yes, sorry, I misread your post - I've edited it now.

 

[snshusat161]

How have you used the formulae you are given? What have you tried to do?

Note that to calculate the potential you must integrate from infinity up to the point that you're concerned about - in this case the formula for the electric field changes between infinity and your point.

Thanks, It is solved now. Actually we have to calculate it in two steps. work required to bring unit positive charge from infinity to the surface and then from surface to some point inside the sphere.

BTW, thanks once again gadje. Sometime a very small hint can trigger our mind.