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:-

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

Choose the thrree coordinate axes as x,y and z and plot the chaerges 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 diiple 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`