A charge `q_(0)` is moved from point P to point q along the arc PQ with centre at O as shown in the figure near a long charged wire. The linear charge density of the wire is `lambda` and it in the same plane. Find the work done in the process.

Explanation

We know that electric field is conservative. So work doen does not depend upon the path.
`W_(P to Q) =W_(P to O) ( :. V_(0)=V_(Q))`
`W_(P to Q) = -int_((r+D))^(D ) q barE . dbarr`
`W= -q int_((r+D))^(D) (2lambda)/(4pi in_(0)) (dr)/(r ) =(lambdaq)/(2pi in_(0)) log_(e ) ((r+D)/(D)).`