Question

# Find the work done by external agent in moving a 1 C charge from point P to Q in presence of an infinitely long uniformly charged line of linear charge density λ as shown.

A
λ2πε0ln1.5
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B
λ2πε0
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C
λ2πε0ln5
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D
7λ2πε0
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Solution

## The correct option is A λ2πε0ln1.5The electric field due to an infinitely long line of charge at a distance r from it is given by |→E|=λ2πε0 r We know that ΔV=−∫r2r1 E dr ΔV=VQ−VP=−∫1.51λ2πε0 r dr=−λ2πε0 (ln1.5−ln1)=−λ2πε0 ln1.5 Change in potential energy: ΔU=ΔV/q ΔU=−λ2πε0 ln1.5 Since, work done is negative of change in potential energy. W=−ΔU=λ2πε0 ln1.5

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