A conducting spherical shell with inner radius a and outer radius b has a positi

Question

A conducting spherical shell with inner radius a and outer radius b has a positive point charge Q located at its center. The total charge on the shell is 3Q , and it is insulated from its surroundings (Figure 1) .

Part A

Derive the expression for the electric field magnitude in terms of the distance r from the center for the region r<a .

Part C

Derive the expression for the electric field magnitude in terms of the distance r from the center for the region a<r<b .

Part D

Derive the expression for the electric field magnitude in terms of the distance r from the center for the region r>b .

Part F

What is the surface charge density on the inner surface of the conducting shell?

Part G

What is the surface charge density on the outer surface of the conducting shell?

Explanation / Answer

Here,

part A) for r < a

the electric field is due to positive charge only

Electric field = k * Q/r^2

part C)

for a < r < b

inside the condutors ,

the electric field is zero under steady state

hence , the electric field is zero for a <r < b

part D)

for r > b

electric field = k * (Q - 3 Q)/r^2

electric field = 2 * k * Q/r^2

part F)

charge on inner surface = - charge placed inside the shell

charge on inner surface = - Q

surface charge density on inner surface = -Q/(4 *pi*a^2)

the surface charge density on inner surface is - Q/(4 *pi*a^2)

part G)

for the outer surafce

charge on outer surface = - 3 Q - (- Q)

charge on outer surface = -2 * Q

surface charge density for outer surface = - 2 *Q/(4 *pi*b^2)

the surface charge density for outer surface is - 2 *Q/(4 *pi*b^2)

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