The Self Potential Energy of Continuous Charge Distributions
Find the elec...
Question
Find the electrostatic energy stored in a cylindrical shell of length l, inner radius a and outer radius b, coaxial with a uniformly charged wire with linear charge density λ.
A
U=λ2l8πε0log(ba)
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B
U=λ2l2πε0log(ba)
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C
U=λ2l4πε0log(ab)
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D
U=λ2l4πε0log(ba)
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Solution
The correct option is DU=λ2l4πε0log(ba) For this we consider an elemental shell of radius x and width dx. The volume of this shell dV can be given as dV=(2πxl)dx
The electric field due to the wire at the shell is E=λ2πε0x
The electrostatic field energy stored in the volume of this shell is dU=[12ε0E2]dV
⇒dU=12ε0(λ2πε0x)2(2πxl)dx
The total electrostatic energy stored in the above mentioned volume can be obtained by integrating the above expression within limits from a to b as