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AP® Physics C: E & M

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Difficult

$E$ Outside Cylinder 3

APPHEM-GKBK3W

The diagram shows the cross-section of a long cylinder having radius $R$. The charge carried by the cylinder is NOT uniform; the charge density varies with radius according to the equation $\rho = \dfrac{A}{\sqrt{r}}$.

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

A

$\dfrac{A\,\sqrt{R}}{\pi \,\epsilon_0\,r}$

B

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

C

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

D

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

E

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