Question

A configuration consists of charges +q, −2q, and +q at the vertices of an equilateral triangle with side length 2l. Treating this as a combination of two dipoles, what is the net dipole moment?

Options

• 4ql

• 2√3 ql

• √3 ql

• ql

Answer 1

This configuration can be decomposed into two dipoles, each with moment \[p_1 = p_2 = q \times 2l\]. The two dipole moments are oriented at 60° to each other (since the interior angles of an equilateral triangle are 60°). Adding the components: \[p = p_1 \cos(30°) + p_2 \cos(30°) = 2 \times q(2l) \times \frac{\sqrt{3}}{2} = 2\sqrt{3}ql\]