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  4. Three point charges of + 2q, + 2q and - 4q are placed at the corners A, B and C of an equilateral triangle ABC of side 'x'. The magnitude of the electric dipole moment of this system is

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Q. Three point charges of $+ 2q, + 2q$ and $- 4q$ are placed at the corners $A, B$ and $C$ of an equilateral triangle $ABC$ of side $'x'$. The magnitude of the electric dipole moment of this system is

KCETKCET 2017Electric Charges and Fields

Solution:

According to question.
The magnitude of electric dipole moment
image
$ P_{\text {net }}=\sqrt{p^{2}+p^{2}+2 p p \cos 60^{\circ}}$
$=\sqrt{2 p^{2}+2 p^{2} \times \frac{1}{2}} $
$=\sqrt{3} \cdot p $
We know that, $ p=2 q \cdot x $
$[\because p=q \cdot I]$
$=\sqrt{3} \cdot 2q x=2 \sqrt{3} \,q x $