Question

find out the work done in bringing a charge q from perpendicular distance r1 to r2

Answer 1

Here is the solution

Answer 2

Work done in bringing the charge q from a distance of the perpendicular $\bold{r_{1}}$ to $\bold{r_{2}}$ is  $\bold{k q_{1} q_{2}\left[\frac{1}{r_{2}}-\frac{1}{r_{1}}\right]}$

Solution:

Work done in  the bringing a charge from a point r1 to a point r2 which is perpendicular to each other is calculated as follows,

The point charge q at distance $r_{1}$ be taken as $q_{1}$

The point charge q at a distance $r_{2}$ be taken as $q_{2}$.

As we know that, dW = F. dx

$\begin{array}{l}{\int_{0}^{W} W=\int_{r_{1}}^{r_{2}} k \frac{\left(q_{2}\right)\left(q_{2}\right)}{x^{2}} d x} \\ \\{W=k q_{1} q_{2}\left(\frac{1}{x}\right)_{r_{1}}^{r_{2}}} \\ \\ \bold{{W=k q_{1} q_{2}\left[\frac{1}{r_{2}}-\frac{1}{r_{1}}\right]}\end{array}}$