Question

Electric charges q q - 2 q are placed at the corners of an equilateral triangle abc of side l the magnitude of equal equal electrical dipole moment of system is

Answer 1

we know, dipole is a system of two opposite nature charge placed in small distance. here in figure, you can see that two dipole are formed and angle between two dipoles is 60° because triangle is an equilateral triangle.

so, magnitude of electrical dipole moment system = $\sqrt{P_1^2+P_2^2+2P_1P_2cos60^{\circ}}$

here, $P_1=P_2=P=ql$

so, Pnet = $\sqrt{P^2+P^2+2P^2cos^{\circ}}$

=$\sqrt{2P^2+P^2}$

=$\sqrt{3}P$

now putting P = ql

so, Pnet = √3ql