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Charges of +q, +q and -2q are fixed at the three vertices A, B and C of an equilateral triangle of side l. What is the magnitude of the net electric dipole moment of this charge configuration?

1. q*l
2. 2*q*l
3. sqrt(3)*q*l
4. 4*q*l

Correct answer: sqrt(3)*q*l

Solution

Split the -2q at C into two -q charges. The +q at A with one -q gives a dipole moment p1 = q*l directed from A toward C; the +q at B with the other -q gives p2 = q*l directed from B toward C. The angle between these two dipole vectors is 60 degrees (the triangle's vertex angle at C). The resultant magnitude = sqrt(p1² + p2² + 2*p1*p2*cos60) = sqrt(q² l² + q² l² + 2 q² l² * 0.5) = sqrt(3) q l.

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