For an infinite line of charge having charge density A lying along x-axis, the work done in moving charge from C to A along arc CA is :

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qλ2πε0loge2

qλ4πε0loge2

qλ2πε0loge12

answer is A.

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Detailed Solution

As E =2λ4πε0r so F=2qλ4πε0r W=∫F dr=∫a2a2qλ4πε0rdr =qλ2πε0∫a2adrr=qλ2πε0(In r)a2a=qλ2πε0In 2a-In a =qλ2πε0 In 2aa=qλ2πε0 In 2