Question

32. Electric charges q,q, - 2q are placed at the corners of
an equilateral triangle ABC of side 1. The magnitude of
electric dipole moment of the system is
(a) al
(b) 2q1
(c) √3ql
(d) 491​

Answer 1

Let A, B and C be the vertices of the triangle.

The charges at the vertices are :

A = q

B = q

C = -2q

The charge at C can be written as : - q + - q

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

Let dipole moment from C to A = P₁ and dipole moment from C to B = P₂

The charge of C is thus split into two that is : - q and - q one king to A and the other one going to A.

The charge q of A + charge - q of C = q

The charge q of B + charge of - q of C = q

Dipole moment (P) =qa where a is the side of the equilateral triangle

P₁ = qa

P₂ = qa

The angle between the dipole moment = 60°

The resultant dipole moment (P) :

P = √(P² + P² + 2P Cos 60° = √3P

P= qa

The answer is thus :

√3qa