Question

Suppose the z axis is uniformly charged with a constant charge density λ. Calculate
the work done to bring a charge Q from a distance y = y2 to y = y1 along y axis.

Answer 1

Answer

Elecric field due to uniformly charged with a constant charge density λ. Is given

$dE=\frac{2k\lambda}{r}dr$

Work done is given by

$dW=QdE$

So total work done

$W=\int^{y_2}_{y_1} Q\frac{2k\lambda }{r}dr$

$W=2kQ\lambda \ln{ (\frac {y_2}{y_1})}$