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Question

Three charges are arranged on the vertices of an equilateral triangle, as shown in the figure. Find the dipole moment of the combination.

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Solution

The system can be considered as a combination of two dipoles making an angle of 60 with each other.

Length of each dipole = d
So, the dipole moment, P = q × d
So, the resultant dipole moment,
Pnet=P2+P2+2Pcos60° =(qd)2+(qd)2+2qd2cos60° =[d2q2+d2q2+2q2d2×12]1/2 =[3q2d2]1/2=3qd
The net dipole moment is along the bisector of the angle at +q, away from the triangle.

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