There is infinitely long straight thread carrying a charge with linear density `lambda`.Calculate the potential difference `A` and `B`.

Explanation

The electric field at perpendicular `x` from wire
`vec(E ) = (lambda)/(2 pi in_(0) x) hat(i) , dx hat(i) + dyhat(j) + dz hat(k)`
`vec(E ). d vec(r ) = (lambda)/(2 pi in_(0) x) dx`
`V_(A) - V_(B) = - int_(eta d)^(d) vec(E) . dvec(r ) = -int_(eta d)^(d) |log_(e ) x|_(eta d)^(d)`
` = - (lambda)/(2 pi in_(0)) log_(e ) ((1)/(eta))`
`= (lambda)/(2 pi in_(0)) log_(e ) (eta)`