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Difficult

$E$ Outside Sphere 2

APPHEM-XSWJEY

The diagram shows a sphere of radius $R$ that has a charge density described by the function $\rho = A\,r$.

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

$\dfrac{A\,{R}^{2}}{8\,\pi \,\epsilon_0\,{r}^{2}}$

B

$\dfrac{A\,{R}^{4}}{3\,\epsilon_0\,{r}^{2}}$

C

$\dfrac{A\,{R}^{4}}{3\,\epsilon_0\,{r}^{2}}$

D

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

E

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