Question

Three 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) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are :

• A. $\sqrt{2qa}$ along + y direction
• B. $\sqrt{2qa}$ 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. $\sqrt{2qa}$ along + x direction

Answer 1

The correct option is B $\sqrt{2qa}$ along the line joining points

(x=0,y=0,z=0) and (x=a,y=a,z=0)
The given charge assembly can be represented using the three co-ordinate axes x, y and z as shown in figure.
The charge -2q is placed at the origin O. One + q charge is place at (a,0, 0) and the other +q charge is placed at(0, a, 0). Thus the system has two dipoles along x-axis and y-axis respectively.
As the electric dipole moment is directed from the negative to the positive charge hence the resultant dipole moment will be along OA where co-ordinates of point A are (a, a, 0). The magnitude of each dipole moment,

, $p=qa$

So, the magnitude of resultant dipole moment is

$P_R=\sqrt{p^2+P^2}=\sqrt{(qa{)}^2+(qa{)}^2}=\sqrt{2}qa$