| 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 12-Jan-2019 Morning] |
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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 :
| [d] 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) |
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| 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, |
| \[2p\cos {{30}^{o}}(-\hat{j})=2(ql)\left( \frac{\sqrt{3}}{2} \right)(-\hat{j})=-\sqrt{3}ql\hat{j}.\] |
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