Question

Three point charges of + 2q, + 2q and - 4q are placed at the corners a, b and c of an equilateral triangle abc of side ‘x'. the magnitude of the electric dipole moment of this system is

Answer 1

We know that two point charges having charge +q and  −q separated by a distance d, constitute an electric dipole. The magnitude of electric dipole moment p is given by
p = q d

It is directed from the negative to the positive charge.
In the given question charge -4q placed at corner c can be thought of two charges -2q placed at c.
As such pair of charges +2q at corner a and -2q at c constitute an electric dipole.
Its dipole moment
[tex]p_{ac}=2qx[tex], directed along ac.

Similarly, second pair of charges +2q at corner b and -2q at c constitute another electric dipole.
Its dipole moment
[tex] p_{bc}=2qx [tex], directed along bc

As abc is an equilateral triangle, the angle between two momenta is =60 deg
Magnitude of the resultant dipole moment is

[tex] p_{resultant}=\sqrt{(2qx)^{2}+(2qx)^{2}+2(2qx)(2qx)\frac{1}{2}} =2\sqrt{3} qx[/tex]
as cos 60 deg =[tex]\frac{1}{2}[tex]