Question

System given below is composed of the charges 10 q , 8 q and -5 q . Find the total electric potential energy of the system of charges .

Answer 1

Given:

System given below is composed of the charges 10 q , 8 q and -5 q .

To find:

Net potential energy of system ?

Calculation:

Lets calculate the potential energy between charge pairs :

$\therefore \: E_{12} = \dfrac{k(10q)( - 5q)}{3d}$

$\implies\: E_{12} = \dfrac{( - 50)k {q}^{2} }{3d}$

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$\therefore \: E_{23} = \dfrac{k( - 5q)(8q)}{5d}$

$\implies \: E_{23} = \dfrac{( - 40)k {q}^{2} }{5d}$

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$\therefore \: E_{31} = \dfrac{k( 8q)(10q)}{4d}$

$\implies \: E_{31} = \dfrac{(80)k {q}^{2} }{4d}$

Now, net potential energy:

$\implies \: E_{net} = \dfrac{( - 50)k {q}^{2} }{3d} + \dfrac{( - 40)k {q}^{2} }{5d} + \dfrac{(80)k {q}^{2} }{4d}$

$\implies \: E_{net} = \dfrac{( - 280)k {q}^{2} }{60d}$

$\implies \: E_{net} = \dfrac{( - 14)k {q}^{2} }{3d}$

So, final answer:

$\boxed{ \bf\: E_{net} = \dfrac{( - 14)k {q}^{2} }{3d} }$