The are AB with the centre C and infinitely long wire having linear charge density `lambda` are lying in the same plane. The minium amount of work to be done to move a point charge `q_(0)` from point A to B through a circular path AB of radius a is equal to

Options

A. `(q_(0)^(2))/(2pi epsilon_(0)) log((2)/(3))`
B. `(q_(0)lambda)/(2pi epsilon_(0)) log((3)/(2))`
C. `(q_(0)lambda)/(2pi epsilon_(0))log((2)/(3))`
D. `q_(0)lambda//sqrt(2) pi epsilon_(0)`

Answer

B

Explanation

`W_(Ararr B) = q (V_(B) - V_(A))`
`= q int_(B)^(A) E.dr`
`=q_(0) int_(2a)^(3a) (lambda)/(2pi epsilon_(0)r) dr`
`= (lambda q_(0))/(2pi epsilon_(0)) ln.(3)/(2)`