AP® Physics C: E & M

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Difficult

$E$ Inside Sphere 3

APPHEM-ZGHFEI

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

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

A

$E = \dfrac{A}{2\,\epsilon_0\,r}$

B

$E = \dfrac{A}{2\,\epsilon_0}$

C

$E = \dfrac{2\,A}{\epsilon_0}$

D

$E = \dfrac{A}{3\,\epsilon_0}$

E

$E = \dfrac{A}{4 \pi \epsilon_0 r}$