Question

Find the energy stored in a mentallic spherical of radius a as charge Q upto distance r=5a

Answer 1

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Question

A total charge Q is distributed uniformly into a spherical volume of radius R . Find the electrostatic energy of this configuration.

Answer · 2 votes

Given a total charge Q is distributed uniformly into a spherical volume of radius R . We have to find the electrostatic energy of this configuration.For this we use the formula, the electrostatic energy Vo = int ε02E^2dl where, ε 0 = permeability of free space E = electric field dl = Volume element For this the electric field can be easily found from Gauss' Theorem to be, E = Q4piε0 × rR^3 & (rR) The two intergrals needed are: int0^R (rR^3)^2 4pi r^2dr = 4pi5R intR^∞ (1r^2)^2 4pi r^2dr = 4piR So, we obtain Vo = int0^∞ ε02E^2 4pi r^2dr [dτ = 4pi r^2dr] So, Vo = ε02 (Q4piε0)^2 ( 4pi5R + 4piR ) Vo = 35 14piε0 Q^2R = 320 Q^2piε0R

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Answer 2

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