1. ## potential

Find the potential inside and outside a uniformly charge sphere of radius $R$ and whose total charge is $q$. Use infinity as your reference point.

So $V(r) = -\int_{\infty}^{r} \bold{E} \cdot d \bold{l}$. What is the electric field inside the sphere?

Then outside the sphere $\bold{E} = \frac{1}{4 \pi \epsilon_{0}} \frac{q}{r^2} \bold{r}$. Then $V(r) = -\int_{\infty}^{r} \bold{E} \cdot d \bold{l} = \frac{q}{4 \pi \epsilon_{0}} \frac{1}{r}$.

For inside the sphere how would you compute the potential?

2. Originally Posted by heathrowjohnny
Find the potential inside and outside a uniformly charge sphere of radius $R$ and whose total charge is $q$. Use infinity as your reference point.

So $V(r) = -\int_{\infty}^{r} \bold{E} \cdot d \bold{l}$. What is the electric field inside the sphere?

Then outside the sphere $\bold{E} = \frac{1}{4 \pi \epsilon_{0}} \frac{q}{r^2} \bold{r}$. Then $V(r) = -\int_{\infty}^{r} \bold{E} \cdot d \bold{l} = \frac{q}{4 \pi \epsilon_{0}} \frac{1}{r}$.

For inside the sphere how would you compute the potential?
Read Example 4.1: Electric field of a uniformly charged sphere and http://physics.bu.edu/~duffy/semeste...l_spheres.html.

3. Originally Posted by heathrowjohnny
Find the potential inside and outside a uniformly charge sphere of radius $R$ and whose total charge is $q$. Use infinity as your reference point.

So $V(r) = -\int_{\infty}^{r} \bold{E} \cdot d \bold{l}$. What is the electric field inside the sphere?

Then outside the sphere $\bold{E} = \frac{1}{4 \pi \epsilon_{0}} \frac{q}{r^2} \bold{r}$. Then $V(r) = -\int_{\infty}^{r} \bold{E} \cdot d \bold{l} = \frac{q}{4 \pi \epsilon_{0}} \frac{1}{r}$.

For inside the sphere how would you compute the potential?
Gauss' Law usually works well...

-Dan