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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,
\[P_{net} = \sqrt{P^2 + P^2 + 2P\cos60^\circ}\]
\[ = \sqrt{(qd )^2 + (qd )^2 + 2 \left( qd \right)^2 \cos60^\circ}\]
\[ = [ d^2 q^2 + d^2 q^2 + 2 q^2 d^2 \times \frac{1}{2} ]^{1/2} \]
\[ = [3 q^2 d^2 ]^{1/2} = \sqrt{3}qd\]
The net dipole moment is along the bisector of the angle at +q, away from the triangle.
Notes
Figure is missing in the question .
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