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AP® Physics C: E & M

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Moderate

$E$ Inside Cylinder 1

APPHEM-JXBJSH

The diagram shows a cylinder of radius $R$ that carries a charge that is uniformly distributed throughout its volume. The cylinder has a charge per unit length of $\lambda$.

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

A

$E=\dfrac{\lambda\,{R}^{2}}{\pi \,\epsilon_0\,{r}^{4}}$

B

$E=\dfrac{\lambda}{2\pi\epsilon_0\,r}$

C

$E=\dfrac{\lambda}{\pi \,\epsilon_0\,{R}^{2}}$

D

$E=\dfrac{\lambda\,r}{2\,\pi \,\epsilon_0\,{R}^{2}}$

E

$E=\dfrac{\lambda\,{R}^{2}}{2\,\pi \,\epsilon_0\,{r}^{3}}$