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Question

# Determine the electric dipole moment of the system of three charges,placed on the vertices of an equilateral triangle ,as shown in the figure:

A
(ql)^i+^j2
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B
3ql^j^i2
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C
3ql^j
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D
2ql^j
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Solution

## The correct option is C −√3ql^jStep 1:Breaking the Charge -2qMake the dipoles out of the given system of charges by breaking up charge −2q as −q and −q as shown in Figure Step 2: Dipole moments of the dipole formedWe know that the direction of a dipole is from −q to q. Now we have two dipole vectors →P1 and →P2 as shown in Figure. Magnitude of dipoles: P1=ql, P2=ql∴P1=P2=P=qlStep 3: Resultant dipole moment As sine components of P1 and P2 would cancel each other.Net dipole moment =Pcos30o(−^j)+Pcos30o(−^j) =−2qlcos30o^j=−√3ql^j Hence, Option (C) is correct.

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