Three points charges $+q,-2 q$ and $+q$ are placed at points $(x=0, y=a, z=0),(x=0, y=0, z=0)$ and $\quad(x=a, y=0, z=0)$, respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

• A

  $\sqrt{2} q a$ along $+y$ direction
• Correct answer
  B

  $\sqrt{2} q a$ along the line joining points $(x=0, y=0, z=0) \text { and }(x=a, y=a, z=0)$
• C

  qa along the line joining points $(x=0, y=0, z=0)$ and $(x=a, y=a, z=0)$
• D

  $\sqrt{2} q a$ along $+x$ direction

Solution

$O$ is the origin at which $-2 q$ 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 $O P$ where $P=(a, a, 0)$. The magnitude of resultant dipole moment is $p^{\prime}=\sqrt{p^2+p^2}=\sqrt{(q a)^2+(q a)^2}=\sqrt{2} q a$

Hence, the correct answer is option: 'B'.