Question

# The arc AB with the centre C and the infinitely long wire having linear charge density λ are lying in the same plane. A point charge qo moves from point A to B through a circular path AB of radius a, then

A
Electric potential at A> Electric potential at B
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B
Minimum amount of work done will be qoλ2πϵoln(3/2)
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C
Minimum amount of work done will be qoλ2πϵoln(2/3)
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D
Electric potential at A< Electric potential at B
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Solution

## The correct option is D Electric potential at A< Electric potential at B Work done, W=qo(VB−VA)=qo(VC−VA) ...(i) Also, dV=−E.dr So, ∫ACdV=−∫3a2aλ2πϵordr ⇒VA−VC=−λ2πϵoln(3/2) ⇒VC−VA=λ2πϵoln(3/2) ...(ii) ⇒W=qoλ2πϵoln(3/2) [From (i)] Hence, option (A) is correct. From figure, VC=VB From (ii), VC−VA=VB−VA>0 ⇒VB>VA Therefore, option (D) is also correct.

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