First slide

Electrostatic potential energy

Question

Three charges $Q, + q and + q$ are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic energy of the configuration is zero if Q is equal to

Moderate

A

$\frac{- q}{1 + \sqrt{2}}$
B

$\frac{- 2 q}{2 + \sqrt{2}}$
C

$- 2 q$
D

+q

Solution

Net electrostatic energy $U = \frac{kQq}{a} + \frac{{kq}^{2}}{a} + \frac{kQq}{a \sqrt{2}} = 0$
$\Rightarrow \frac{kq}{a} (Q + q + \frac{Q}{\sqrt{2}}) = 0 \Rightarrow Q = - \frac{2 q}{2 + \sqrt{2}}$

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