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 :
qλ2πε0loge2
qλ4πε0loge2
qλ2πε0loge12
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