SATHEE: Electric Charges and Fields - Result Question 23

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

[2007]

(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 $+ v e x$ direction

(d) $\sqrt{2} q a$ along + ve $y$ direction

Show Answer

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 $\vec{O A}$ and other along $\vec{O B}$ . Hence, net dipole moment, $p_{net} = \sqrt{(q a)^{2} + (q a)^{2}} = \sqrt{2} q a$ along $\vec{O P}$ at an angle $45^{\circ}$ with positive $X$ -axis.

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