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

The center of charge of two point charges each of magnitude -q placed at B and C will be at the mid point of BC . Let this point be D. The effective charge at B will be -2q.

So the dipole system will be due to positioning of two point charges of magnitude `+2q` at A and `-2q` at D. The distance AD is the height of the equilateral triangle ABC of side `x`.

So `AD=sqrt3/2x`

Hence the dipole moment of the system `=2qxxsqrt3/3x=sqrt3qx`

Alternative way

The system may also be considered as composed of two dipoles 'AC' and 'BC' each having moment of magnitude `p=qx` and they are aligned at an angle `theta =60^@`

So resultant dipole moment will be

`p_"reultant"=sqrt(p^2+p^2+2p^2cos60^@)=sqrt3p=sqrt3qx`