Question

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?

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 `+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`