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Energy Stored In Electrostatic Field

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Find the energy stored in the electrostatic field of a uniformly charged (with density p) spherical shell of inner radius a and outer radius b.

Sphere of what Radius R in space contains half of that energy?

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Solution Summary

The energy stored in the electric field due to a charged hollow sphere is calculated.

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Electrostatic Field
Find the energy stored in the electrostatic field of a uniformly charged (with density p) spherical shell of inner radius a and outer radius b.
Sphere of what Radius R in space contains half of that energy?

Solution:
The energy density or the energy stored per unit volume in an electrostatic field E is given by
u= 1/2 ϵ_0 E^2
The shell is charged uniformly thus it is non-conducting and the permittivity to be considered unity.
1. Due to symmetry of charge distribution and according to Gauss law the field inside the shell will be zero and thus energy stored inside the shell (r < a) U1 will be zero.
2. The field within the conductor at a distance r from the center of the shell (a < r < b) can be calculated using Gauss's law by considering a Gaussian loop of concentric circle of radius r as
∮▒E ⃗ .ds=q_inloop/ϵ_0
...

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