question_answer

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]

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)   \[-\sqrt{3}ql\,\hat{j}\]

Correct Answer: D

Solution :

The given system of charges can be considered to consists of two dipoles of charges\[+q\,\,and\,\,-q\]. 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, \[2p\cos {{30}^{o}}(-\hat{j})=2(ql)\left( \frac{\sqrt{3}}{2} \right)(-\hat{j})=-\sqrt{3}ql\hat{j}.\]