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