Electricity and Magnetism

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Difficult

Electric Fields from Exponential Charge Distributions

EANDM-BIF9XE

A sphere is centered at the origin with a radius $a$. The material is non-conducting and has a radially dependent charge density given by $\rho (r) = \rho_o e^{-r^3 / a^3}$.

What is the electric field for all $r > a$?

A

$E(r>a)=(0.37)\bigg( \cfrac{ 4 \pi \rho_o a^3}{3 \epsilon_o r^2} \bigg)$

B

$E(r>a)=(0.63)\bigg( \cfrac{4 \pi \rho_o a^3}{3 \epsilon_o r^2} \bigg)$

C

$E(r>a)=(0.37)\bigg( \cfrac{ \rho_o a^3}{3 \epsilon_o r^2} \bigg)$

D

$E(r>a)=\bigg( \cfrac{ \rho_o a^3}{3 \epsilon_o r^2} \bigg)$

E

$E(r>a)=(0.63)\bigg( \cfrac{ \rho_o a^3}{3 \epsilon_o r^2} \bigg)$