Three charges are arranged on the vertices of an equilateral triangle as shown in figure. Find the dipole moment of the combination.

Consider an equilateral triangle of side I. Point A and B have charges ( +mathrm{q} ) where ( mathrm{A} ) has ( -2 mathrm{q} ) charge. The system as two dipoles with ( overrightarrow{mathrm{p}}_{1} ) and
( vec{p}_{2} )
along BA and CA respectively. Hence, the magnitude of ( overrightarrow{mathrm{p}}_{1} )
and
( vec{p}_{2} )
are equal to (qI) and the angle between them is ( 60^{circ} . ) Therefore
the resultant of two is the net dipole moment.
( overrightarrow{mathrm{P}}=sqrt{mathrm{P}_{1}^{2}+mathrm{P}_{2}^{2}+2 mathrm{P}_{1} mathrm{P}_{2} cos 60^{circ}}=sqrt{mathrm{q}^{2} mathrm{I}^{2}+mathrm{q}^{2} mathrm{I}^{2}+2 mathrm{q}^{2} mathrm{I}^{2}(1 / 2)} )
( P=q I sqrt{3} )