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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.
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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