Q.
Three point charges +q,2q and +q are placed at points (x=0,y=a,z=0),(x=0,y=0,z=0) and (x=a,y=0, z=0 ), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are
Electric dipole moment is a vector quantity directed from negative charge to the similar positive charge. Choose the three coordinate axes as x,y and z and plot the charges with the given coordinates as shown. O is the origin at which −2q charge is placed. The system is equivalent to two dipoles along x and y-directions, respectively. The dipole moments of two dipoles are shown in figure.
The resultant dipole moment will be directed along OP where P=(a,a,0). The magnitude of resultant dipole moment is p′=p2+p2 =(qa)2+(qa)2=2qa