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Electricity and Magnetism

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Moderate

Fields from Spheres with Conductors

EANDM-1KSHLF

A spherically symmetric sphere, centered at the origin, has a central core (region 1) of radius $r_1$ surrounded by a thick shell (region 2) between $r_1 < r < r_2$, as shown in the accompanying figure. The core is made of a non-conducting material with a constant charge density of $\rho_1$. The shell is a conducting metal with no additional charge.

What is the electric field for $r_1 < r < r_2$ (region (2)?
What is the electric field for $r> r_2$ (outside of the sphere)?

Created for Albert.io. Copyright 2016. All rights reserved.

A

Region (2) $E(r)=\cfrac{\rho_1 r_2 ^3}{3 \epsilon_o r^2} \, N/C$
Region outside of sphere: $E(r)=0 \, N/C$

B

Region (2) $E(r)=\cfrac{\rho_1 r_1 ^3}{3 \epsilon_o r^2} \, N/C$
Region outside of sphere: $E(r)=\cfrac{\rho_1 r_2 ^3}{3 \epsilon_o r^2} \, N/C$

C

Region (2) $E(r)=0 \, N/C$
Region outside of sphere: $E(r)=\cfrac{\rho_1 r_1 ^3}{3 \epsilon_o r^2} \, N/C$

D

Region (2) $E(r)=0 \, N/C$
Region outside of sphere: $E(r)=0 \, N/C$