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)lambda)/(2pi in_(0))ln 3/2`
B. `(q_(0)lambda)/(4pi in_(0))ln 2`
C. `(q_(0)lambda)/(pi in_(0))ln 3/2`
D. `(q_(0) lambda)/(2pi in_(0))`

Answer

C

Explanation

`W_("ext")=-(Klambda)/(r) underset(r_(A))overset(r_(B))(int) r_(B)/r_(A)`
`W_("ext")=-K lambda ln r_(B)/r_(A)`