Three charges q, -2q and q are placed at three vertices of an equilateral triangle. Determine the equivalent dipole moment of the system.

Explanation

The given system is a combination at two dipoles at an angle ` 60 ^@ ` with each other.

Let the dipole moment of one dipole is `p _ 1 ` and that of another dipoles is ` p _ 2 ` , the length of each side of the equilateral triangle is a.
` therefore ` Equivalent dipole moment,
` p = p _ 1 cos 30 ^@ + p _ 2 cos 30^@ `
[` because ` since components cancel each other ]
` = 2qa cos 30 ^@ " "[ because p _ 1 = p _ 2 = qa ]`
` = 2 q a xx ( sqrt3 ) / ( 2 ) = sqrt 3 qa `