Two charges of -4 and +4 are placed at the points A(1, 0, 4) m and B(2, -1, 5) m located in an electric field E = 0.20i V/cm. The magnitude of the torque acting on the dipole is 8√(α) × 10⁻⁵ Nm, where α = _________. Numerical answer type. Work it out, then open the answer.

Answer: 2. d = B - A = ( i - j + k) m, so p = 4×10⁻⁶( i - j + k) C m. E = 0.20 V/cm = 20 i V/m τ = p× E = 8×10⁻⁵ ( i - j + k)× i = 8×10⁻⁵( j + k) |τ| = 8√2×10⁻⁵ N m, so α = 2.

Two charges of -4 and +4 are placed at the points A(1, 0, 4) m and… | JEE Main 2024 (27 Jan, Shift 2)

Q37JEE Main 2024 · 27 JAN · SHIFT 2Medium

Electric Dipole

Two charges of $-4\,\mu\text{C}$ and $+4\,\mu\text{C}$ are placed at the points $A(1, 0, 4)\text{ m}$ and $B(2, -1, 5)\text{ m}$ located in an electric field $\vec{E} = 0.20\hat{i}\text{ V/cm}$ . The magnitude of the torque acting on the dipole is $8\sqrt{\alpha} \times 10^{-5}\text{ Nm}$ , where $\alpha =$ _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 2

$\vec d = \vec B - \vec A = (\hat i - \hat j + \hat k)$ m, so $\vec p = 4\times10^{-6}(\hat i - \hat j + \hat k)$ C m.
$\vec E = 0.20$ V/cm $= 20\,\hat i$ V/m
$\vec\tau = \vec p\times\vec E = 8\times10^{-5}\,(\hat i - \hat j + \hat k)\times\hat i = 8\times10^{-5}(\hat j + \hat k)$
$|\vec\tau| = 8\sqrt2\times10^{-5}$ N m, so $\alpha = 2$ .

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Electric Dipole question from JEE Main 2024 (27 Jan, Shift 2)

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