Three point charges of +2q, -q and -q are placed at the corners A, B and C of an equilateral triangle ABC of side ‘x’. What is the magnitude of the electric dipole moment of this system?

1 Answer
Apr 27, 2018

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 +2q placed at point A can be thought of two charges +q placed at A.
As such pair of charges +q at A and -q at B constitute an electric dipole.
Its dipole moment

vecp_(AB)=qx, directed along BA

Similarly, second pair of charges +q at A and -q at C constitute another electric dipole.
Its dipole moment

vecp_(AC)=qx, directed along CA

As ABC is an equilateral triangle, the angle between two momenta is =60^@
Magnitude of the resultant dipole moment is

|vecp_"resultant"|=sqrt(p_(AB)^2+p_(AC)^2+2\ p_(AB)\ p_(AC)\ cos60^@)
|vecp_"resultant"|=sqrt((qx)^2+(qx)^2+2qx xx qx xx1/2)=sqrt3qx