Question

Electric charge q q and -2q respectively are placed at the three corners of an equilateral triangle of side
a.Magnitude of the electric dipole moment of the system is

Answer 1

Let A,B,C be the vertices of an equilateral triangle of side L.

The charges are placed at the vertices of the triangle as shown in the figure.  

Let u separate the -2q charge at C as -q and -q.

Dipole moment is always from a negative charge to a positive charge.  

Dipole Moment P = q x length = qL.

-q at C forms a dipole with +q at A. Hence p1 = qL.

-q at C forms a dipole with +q at B. Hence p2 = qL.

Both dipoles are at 60° angle.  

The resultance dipole p = √(p1² + p2² + 2*p1*p2*cos(60))

= √((qL)² + (qL)² + 2*qL*qL*cos(60))

Simplifying you get P =√(3)*qL