JEE PYQ: Electrostatics Question 61
Question 61 - 2019 (12 Jan Shift 2)
Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure:
(1) $\sqrt{3};ql;\frac{\hat{i} - \hat{j}}{\sqrt{2}}$
(2) $(ql)\frac{\hat{i} - \hat{j}}{\sqrt{2}}$
(3) $2ql;\hat{j}$
(4) $-\sqrt{3}ql;\hat{j}$
Show Answer
Answer: (4)
Solution
With $+q$ at two base corners and $-2q$ at top: the dipole moment of the pair of $+q$ charges with the $-2q$ gives a resultant. Computing: $|\vec{P}_{\text{resultant}}| = 2P\cos 30° = 2ql \times \frac{\sqrt{3}}{2} = \sqrt{3}ql$, directed downward: $\vec{P} = -\sqrt{3}ql;\hat{j}$.
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