Question

Three point charges $+q, 2 q$ 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

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

Answer 1

Answer: (B)

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 $-2 q$ 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$