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. `sqrt2 qa` along + y direction
B. `sqrt2 qa` along the line joining points
`(x = 0, y = 0, z = 0)` and `(x = a, y = a, z = 0)`
C. `aq` along the line joining points
`(x = 0, y = 0, z =0)` and `(x = a, y = a, z = 0)`
D. `sqrt2 qa` along + x direction

Answer

B

Explanation

(b) Electric dipole moment is a vector quantity directed from negative charge to the similar positive charge. Choose the three corrdinate 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 is placed. The system is equivalent to two diploes along `x` and y-directions respecitvely. The dipole moments of two dipolmes are shown in figure.
The resultant dipole moments 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`