Question

# Electric charge q , q and −2q are placed at the corners of an equilateral triangle ABC of side L. The magnitude of electric dipole moment of the system is

A
qL
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B
2qL
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C
3qL
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D
4qL
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Solution

## The correct option is C √3qLStep 1: Breaking the charges In the given situation, we do not se any dipole directly. But we can make dipoles by breaking the charges.So, We Break the −2q charge in two −q charges, and we get two dipoles as shown in the figure.Dipole moment of both dipoles P=qL Step 2: Calculation of net dipole moment Since dipole is vector quantity, so we add the two dipoles vectorially to get the resultant dipole moment.Both dipoles are at angle θ=60∘ So, Resultant Pnet=√P2+P2+2(P)(P)cos60 =√3P2 =√3P Pnet=√3(q×L) Hence, Option (C) is correct.

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