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

a-

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

Express your answer in terms of some or all of the variables Q, a, b, and appropriate constants.

b-

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

Express your answer in terms of some or all of the variables Q, a, b, and appropriate constants.

Explanation / Answer

here,

charge at centre is Q

electric field = electric field due point charge + electric due to inner shell + electric field due to outer shell

part A)

the magnitude of the electric field in the region r <= a , E = K *
Q /r^2

E = Q/(4 * pi * epsilon * r^2)

the magnitude of the electric field in the region r <= a is Q/(4 * pi * epsilon * r^2)

part B)

the magnitude of the electric field in the region r >= b , E = - k * 2Q/r^2 - k *Q/r^2 + k * Q/r^2

E = 2 * k * Q/r^2

E = - 2 * Q / (4 * pi * epsilon * r^2)

the magnitude of the electric field in the region r >= b is - 2 * Q / (4 * pi * epsilon * r^2)

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