Question

Ques: Three point charges 1µC, -1µC, 2µC were initially infinite distance apart. Calculate the work done in assembling

these charges at the vertices of an equilateral triangle of side 10cm (PYQ 2020)​

Answer 1

Given:

Three point charges 1µC, -1µC, 2µC were initially infinite distance apart.

To find:

The work done in assembling these charges at the vertices of an equilateral triangle of side 10cm.

Calculation:

At infinity , net potential energy is:

$PE_{ \infty} = 0$

In the Triangular Configuration, potential energy will be :

$\rm PE_{\Delta } = \bigg \{ \dfrac{k(1)( - 1)}{d} + \dfrac{k(2)( - 1)}{d} + \dfrac{k(1)(2)}{d} \bigg \} \times {10}^{ - 12}$

$\rm \implies PE_{\Delta } = \bigg \{ - \dfrac{k}{d} - \dfrac{2k}{d} + \dfrac{2k}{d} \bigg \} \times {10}^{ - 12}$

$\rm \implies PE_{\Delta } = \bigg \{ - \dfrac{3k}{d} + \dfrac{2k}{d} \bigg \} \times {10}^{ - 12}$

$\rm \implies PE_{\Delta } = \bigg \{ - \dfrac{k}{d} \bigg \} \times {10}^{ - 12}$

$\rm \implies PE_{\Delta } = \bigg \{ - \dfrac{9 \times {10}^{9} }{( \frac{10}{100} )} \bigg \} \times {10}^{ - 12}$

$\rm \implies PE_{\Delta } = \bigg \{ - 9 \times {10}^{10}\bigg \} \times {10}^{ - 12}$

$\rm \implies PE_{\Delta } = - 9 \times {10}^{ - 3} \: J$

So, work done is :

$\rm W = ( - 9 \times {10}^{ - 3} ) - 0$

$\rm \implies W = - 9 \times {10}^{ - 3} \: joule$

Hope It Helps.