Question

Find the work done in bringing a charge q from perpendicular distance r₁ to r₂ (r₂ > r₁)

Answer 1

Let's suppose the charge is moved by an infinitely small distance dr. Small work is done in moving the charge, dw = qdV where V is the Potential difference between the two points.

Now, `dV = intE.dr = -int_(r1)^(r2)  (lambdadr)/(2pirepsilon_0) = lambda/(2piepsilon_0) int_(r1)^(r2) (dr)/r = lambda/(2piepsilon_0) In [r_1/r_2]`

Work done = `qdv = (qlambda)/(2piepsilon_0) In [r_1/r_2]`