The point charges `+ q, -2q` and `+ q` are placed at point `(x = 0, y = a, z = 0), (x = 0, y = 0, z = 0)` and `(x = a, y = 0, z = 0)`, repectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

Options

A. `sqrt(2)qa` along `+y` direction
B. `sqrt(2)qa` along the line joining points `(x-0, y=0,z=0)` and `(x=a,y=a,z=0)`
C. `qa` along the line joining points `(x=0,y=0,z=0)` and `(x=a,y=a,z=0)`
D. `sqrt(2)qa` along `+x` direction

Answer

b

Explanation

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 dipole along `x` and `y`-direction respectively. The dipole moments of two dipoles are shown in the figure.
The resultant dipole moment will be directed along `OP` where `P= (a,a,0)`. The magnitude of resultant dipole moment is
`P'=sqrt(P^(2)+P^(2))=sqrt((qa)^(2)+(qa)^(2))= sqrt(2)qa`