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Electricity and Magnetism

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Moderate

Electric Flux through a Sphere

EANDM-4H3KBM

An electric field has the form $\overrightarrow { E } = 2.5 r^2 \widehat {r}$, where $r$ is the distance from the origin and $\widehat {r}$ is the unit vector that points radially away from the origin.

Calculate the electric flux through the surface of a sphere centered on the origin of radius $R = 7 \text cm$.

A

$1.89 \times {10}^{-4} \: \frac {N m^2}{C}$

B

$7.5 \times {10}^{-4} \: \frac {N m^2}{C}$

C

$7.5 \: \frac {N m^2}{C}$

D

$0.0123 \: \frac {N m^2}{C}$

E

$4.9 \times {10}^{-3} \: \frac {N m^2}{C}$