First slide

Electric dipole

Question

Three charges of (+2q), (- q) and (- q) are placed at the corners A, B and C of an equilateral triangle of side a as shown in the figure. The magnitude of dipole moment of this combination is

Moderate

A

qa
B

Zero
C

$qa \sqrt{3}$
D

$\frac{2}{\sqrt{3}} q a$

Solution

The charge +2q can be broken in +q, +q. Now as shown in figure, we have two equal dipoles inclined at an angle of 60°. Therefore, resultant dipole moment will be $p_{net} = \sqrt{p^{2} + p^{2} + 2 ppcos 60 °}$
$p_{net} = \sqrt{3} p = \sqrt{3} qa$

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