Question

Three charges q,q and -2q are placed at the 3 vertices of an equilateral triangle. Then what is the equivalent dipole moment of the system

Answer 1

The equivalent dipole moment of the system is D.M= 3 / √2 qdi + ( 1 - √2 / √ 2 ) qdj

Explanation:

Since this system of charges is a non-neutral system.

Dipole momentum of system

- 2q (d / √ 2 ) ( - j) + ( - 2q ) (d / √ 2 ) ( -i) + q (d / √ 2 )  + q (d / √ 2 ) (- j )+ (-q)dj

=  √2 qdj + √2 qdi + 1/ √2 qdi - 1/ √ 2 qdj = qdj

= 3 / √ 2 qdi + qdj ( √2 - 1 /√2 - 1 )

= 3 / √2 qdi + ( 1 - √2 / √ 2 ) qdj

The electric potential energy of a system of three point charges  can be calculated in a similar manner

U = 1 / 4πεo ( q1q2 / r12 + q1q3 / r13 + q2q3 / r23)

Thus the equivalent dipole moment of the system is D.M= 3 / √2 qdi + ( 1 - √2 / √ 2 ) qdj