# Compute voltage inside sphere of uniform charge

1. Jan 23, 2014

### Gary Roach

1. The problem statement, all variables and given/known data
Problem 2.21 from Introduction to Electrodynamics, David J. Griffiths, Third Edition.

Find the potential inside and outside a uniformly charged solid sphere who's radius is R and whose total charge is q. Use infinity as your reference point.

2. Relevant equations
Given: q, R, r'(r inside sphere)
Variable: r
∫E da =q/ε0
V = -∫$^{r}_{∞}$E dl

3. The attempt at a solution
Outside of sphere:
|E|∫s r2sinΘdΘdø = (1/ε0)q
E = (q)$\widehat{r}$/(4π εor2)
V = -∫$^{r}_{∞}$E dr =q/4πε0r

The above is pretty straight forward. On the other hand, the Voltage inside the sphere completely illudes me. From the answer book, I know that is an A - B type problem but can't seem to get my mind around the concept. I know that the Voltage is a function of the radius but the E field is not zero as in a hollow sphere. How is the basic equation for the E field inside the sphere derived?

Last edited: Jan 23, 2014
2. Jan 23, 2014

### lightgrav

charge inside the gaussian surface at r<R is proportional to the Volume enclosed: rho V_inside
where rho = q/(4/3 pi R^3)

3. Jan 23, 2014

### Staff: Mentor

For a radius r>R, consider the sphere with a smaller radius (smaller than r) and the hollow sphere with a larger radius (larger than r) as separate objects. How can you calculate their field contributions?