JEE Main 12 Jan 2019 Morning Question 12
Question: Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure. [JEE Main Online Paper Held On 12-Jan-2019 Morning]
Options:
A) $ 2ql,\hat{j} $
B) $ (ql),\frac{\hat{i}+,\hat{j}}{\sqrt{2}} $
C) $ \sqrt{3}ql,\frac{,\hat{j}-\hat{i}}{\sqrt{2}} $
D) $ -\sqrt{3}ql,\hat{j} $
Show Answer
Answer:
Correct Answer: D
Solution:
The given system of charges can be considered to consists of two dipoles of charges $ +qand-q $ .
Let p be the dipole moment by the dipole of charges $ +q and -q $ (placed at point B)
The horizontal components of p (due to charges at A, B and B) cancels each other and vertical components adds up.
So, the net dipole moment of system of charges, $ 2p\cos 30^{o}(-\hat{j})=2(ql)( \frac{\sqrt{3}}{2} )(-\hat{j})=-\sqrt{3}ql\hat{j}. $
