Potential of a uniformyl charged sphere

[ehabmozart]

Homework Statement

The question asks to find the potential due to a uniformly charged sphere at r<R where R is the radius.

Homework Equations

Va-Vb= ∫ E dr from a → b

The Attempt at a Solution

My attempt was like this

Va is to be a the point of interest r.. Vb to be R... We know Vb to be KQ/R... Now E inside the sphere is KQr/R^3 .. After integration with respect to r we get (R^2-r^2)*Kq/2R^3 ... Thus the net potential at Va is Vb + the integral which is KQ/R + (R^2-r^2)*Kq/2R^3 ... However, this isn't the answer given.. Where was my mistake??

 

[mfb]

How does it differ from the answer given?
Note that it is possible to simplify your expression.

 

[ehabmozart]

How does it differ from the answer given?
Note that it is possible to simplify your expression.

I am not able to simplify.. Can you help me?

 

[mfb]

Just use (a-b)/c = a/c - b/c for (R^2-r^2)*Kq/(2R^3).