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# Fields in Spheres with Conductors

EANDM-CKQOHW

A sphere of radius $r_2$ is centered on the origin. It has within it a core of radius $r_1$ as shown in the accompanying figure. The material of the core (region 1) is a conducting metal. Region 2 between $r_1 < r < r_2$ is composed of a non-conducting material. The core is charged with a total charge of $Q_o$. Region 2 has a uniform charge density of $\rho_o$.

What is the value of the electric field in the core, region 1, $r < r_1$?
What is the value of the electric field in region 2, $r_1 < r < r_2$?

A

$E(r > r_1 ) = (\cfrac{1}{4 \pi \epsilon_o (r - r_1 )^2}) \bigg( \cfrac{4 \pi \rho ( r^3 -r_1 ^3 )}{3} \bigg)$

B

$E(r > r_1 ) = (\cfrac{1}{4 \pi \epsilon_o (r - r_1 )^2}) \bigg(Q_o +\cfrac{4 \pi \rho ( r^3 -r_1 ^3 )}{3} \bigg)$

C

$E(r > r_1 ) = (\cfrac{1}{4 \pi \epsilon_o r^2}) \bigg(Q_o +\cfrac{4 \pi \rho ( r^3 -r_1 ^3 )}{3} \bigg)$

D

$E(r > r_1 ) = (\cfrac{1}{4 \pi \epsilon_o r^2}) \bigg(\cfrac{4 \pi \rho ( r^3 -r_1 ^3 )}{3} \bigg)$

E

$E(r > r_1 ) = (\cfrac{1}{4 \pi \epsilon_o r^2}) \bigg(Q_o +\cfrac{4 \pi \rho ( r_1 ^3 )}{3} \bigg)$