Three identical charges are placed at corners of an equilateral triangle of side $l$ . If force between any two charges is $F$ , then the work required to double the dimension of triangle is :

- 3 F l

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3 F l

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(- 3 / 2) F l

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(3 / 2) F l

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Solution

The correct option is C $(- 3 / 2) F l$

The potential energy of three charge system is $U = k [\frac{q_{1} q_{2}}{r_{12}} + \frac{q_{1} q_{3}}{r_{13}} + \frac{q_{2} q_{3}}{r_{23}}]$

when three identical charge q are held at corner of equilateral triangle, the potential energy is

$U_{i} = k [\frac{q q}{l} + \frac{q q}{l} + \frac{q q}{l}] = \frac{3 k q^{2}}{l}$

Force between any two charges is $F = \frac{k q^{2}}{l^{2}} . . . . (1)$

when dimension is doubled $(l = 2 l)$ , the potential energy is

$U_{f} = k [\frac{q q}{2 l} + \frac{q q}{2 l} + \frac{q q}{2 l}] = \frac{3 k q^{2}}{2 l}$

The work done $W =$ change in potential energy $= U_{f} - U_{i} = \frac{3 k q^{2}}{2 l} - \frac{3 k q^{2}}{l} = - \frac{3 k q^{2}}{2 l} = (- 3 / 2) F l$ using (1)

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Three identical charges are placed at corners of an equilateral triangle of side l. If force between any two charges is F, then the work required to double the dimension of triangle is :

Three identical charges are placed at corners of an equilateral triangle of side $l$ . If force between any two charges is $F$ , then the work required to double the dimension of triangle is :