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JEE Main 2019 (12 Jan, Shift 1) · Electric Dipole

Electric Dipole question from JEE Main 2019 (12 Jan, Shift 1)

Q62JEE Main 2019 · 12 JAN · SHIFT 1Easy

Electric Dipole

Determine the electric dipole moment of the system of the three charges, placed on the vertices of an equilateral triangle, as shown in the figure:

Figure

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Answer: (d)

+q (0,0)+q (l, 0)-2q (l/2, √3l/2)xy
  1. Take +q+q at (0,0)(0,0), +q+q at (ℓ,0)(\ell,0) and −2q-2q at (ℓ2,3ℓ2)\left(\frac{\ell}{2},\frac{\sqrt{3}\ell}{2}\right).
  2. Net charge is zero, so p⃗=∑qir⃗i\vec{p} = \sum q_i\vec{r}_i.
  3. p⃗=qℓi^−2q(ℓ2i^+3ℓ2j^)=−3 qℓj^\vec{p} = q\ell\hat{i} - 2q\left(\frac{\ell}{2}\hat{i} + \frac{\sqrt{3}\ell}{2}\hat{j}\right) = -\sqrt{3}\,q\ell\hat{j}
  4. So the answer is (d) −3 qℓj^-\sqrt{3}\,q\ell\hat{j}.
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