?

AP® Physics C: E & M

Free Version

Upgrade subject to access all content

Difficult

$E$ Outside Sphere 3

APPHEM-SSK1XK

The diagram shows a sphere of radius $R$ that has a charge density described by the function $\rho = \dfrac{A}{r^2}$.

Which of the following expressions gives the electric field strength at point $P$, a point that lies outside the sphere and is a distance $r$ from the center of the sphere?

A

$\dfrac{A\,R}{\epsilon_0\,{r}^{2}}$

B

$\dfrac{A\,{R}^{3}}{3\,\epsilon_0\,{r}^{4}}$

C

$\dfrac{A\,R}{3\,\epsilon_0\,{r}^{2}}$

D

$\dfrac{A}{4\,\pi \,\epsilon_0\,R\,{r}^{2}}$

E

$\dfrac{A\,R}{3\,\epsilon_0\,{r}^{2}}$