Question

Three charges are arranged on the vertices of an equilateral triangle as shown in figurre (29-E6). Find the eipole moment of the combination.

Answer 1

Let - q and -q are placed at A and C
where 2q on B
So, length of A = d

So, the dipole moment $=(q\times d)=P$
So, resultant dipole moment
$P=\left[\right(qd{)}^2+(qd{)}^2+2qdqd\cos 60{]}^{\frac{1}{2}}$
$=[d^2{q}^2+d^2{q}^2+2q^2{d}^2\times \frac{1}{2}{]}^{\frac{1}{2}}$
$=[3q^2{d}^2{]}^{\frac{1}{2}}=\sqrt{3}qd$