Question

two charges q1 and q2 are separated by
a distance d. calculate the work done in
increasing the distance to 2d​

Answer 1

Given:

Two charges q1 and q2 are separated by

a distance d.

To find:

Work done in increasing the distance upto 2d.

Calculation:

Initial potential energy between the two charges

$U1 = \dfrac{1}{4\pi \epsilon_{0}} \bigg \{ \dfrac{(q1)(q2)}{d} \bigg \}$

After changing the separation distance to 2d , new Potential Energy:

$U2 = \dfrac{1}{4\pi \epsilon_{0}} \bigg \{ \dfrac{(q1)(q2)}{2d} \bigg \}$

So, work done will be equal to change in Potential Energy of the system:

$\therefore \: work = U2 - U1$

$= > work = \dfrac{1}{4\pi \epsilon_{0}} \bigg \{ \dfrac{(q1)(q2)}{2d} \bigg \} - \dfrac{1}{4\pi \epsilon_{0}} \bigg \{ \dfrac{(q1)(q2)}{d} \bigg \}$

$= > work = - \dfrac{1}{4\pi \epsilon_{0}} \bigg \{ \dfrac{(q1)(q2)}{2d} \bigg \}$

So, final answer is:

$\boxed{ \sf{work = - \dfrac{1}{4\pi \epsilon_{0}} \bigg \{ \dfrac{(q1)(q2)}{2d} \bigg \} }}$

[Since work done is negative, it signifies the fact that it the change in distance between the charged system will be spontaneous.]