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(C) The charge $+2q$ at vertex $A$ can be considered as two charges of $+q$ each. We can form two electric dipoles: one from vertex $A$ to $B$ (with c

Vedclass · Accepted Answer

$q a \sqrt{3}$

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(C) The charge $+2q$ at vertex $A$ can be considered as two charges of $+q$ each. We can form two electric dipoles: one from vertex $A$ to $B$ (with charge $+q$ at $A$ and $-q$ at $B$) and another from vertex $A$ to $C$ (with charge $+q$ at $A$ and $-q$ at $C$). The dipole moment of each dipole is $p = q a$. The angle between these two dipole moments is $60^{\circ}$ (the angle of the equilateral triangle). The resultant dipole moment $p_{net}$ is given by the vector sum: $p_{net} = \sqrt{p^2 + p^2 + 2 p p \cos 60^{\circ}}$ $p_{net} = \sqrt{2p^2 + 2p^2 (1/2)} = \sqrt{3p^2} = p \sqrt{3}$ Substituting $p = qa$,we get $p_{net} = q a \sqrt{3}$.

Charges are placed at the vertices of an equilateral triangle as shown in the figure. What is the resultant dipole moment?

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