Determine the electric dipole moment of the system of three charges placed on the vertices of an . . .

Question : Determine the electric dipole moment of the system of three charges placed on the vertices of an equilateral triangle as shown in the figure. 

a)√3ql(j-i)/√2

b) 2qlj

c) -√3qlj

d) ql(i+j)/√2

Solution : 

Here 
p=ql

Direction of Dipole Moment is from -ve charge to +ve charge as shown in the figure.

Here θ = 30°

Resolving the dipole moment p into two rectangular components pcosθ  and psinθ  as shown in the figure.

So Resultant dipole moment
p_NET = 2pcosθ 
=2(ql)cos30°
=2ql(√3/2)
=√3 ql 

As seen in the figure, the resultant direction will be towards -ve z-axis (-j)
So the final answer will be -√3qlj.

Hence c) -√3qlj will be the correct option.