Electric Charges and Fields - Result Question 23
23. Three point charges $+q,-q$ 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
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(a) $\sqrt{2} q a$ along the line joining points $(x=0, y=0, z=0)$ and $(x=a, y=a, z=0)$
(b) $q a$ along the line joining points $(x=0$, $y=0, z=0)$ and $(x=a, y=a, z=0)$
(c) $\sqrt{2} q a$ along $+ve x$ direction
(d) $\sqrt{2} q a$ along + ve $y$ direction
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Answer:
Correct Answer: 23. (a)
Solution:
- (a) Three point charges $+q,-2 q$ and $+q$ are placed at points $B(x=0, y=a, z=0)$, $O(x=0, y=0, z=0)$ and $A(x=a, y=0, z=0)$ The system consists of two dipole moment vectors due to $(+q$ and $-q)$ and again due to $(+q$ and $-q$ ) charges having equal magnitudes qa units - one along $\overrightarrow{{}O A}$ and other along $\overrightarrow{{}O B}$. Hence, net dipole moment, $p _{\text{net }}=\sqrt{(q a)^{2}+(q a)^{2}}=\sqrt{2} q a$ along $\overrightarrow{{}O P}$ at an angle $45^{\circ}$ with positive $X$-axis.
