Electrostatics

JEE Main level, single correct, medium

239 of 311

Question 239 of 311

A dipole with two electric charges of 2μC2 \mu \mathrm{C} magnitude each, with separation distance 0.5μ m0.5 \mu \mathrm{~m}, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30∘30^{\circ} from the axis, it tends to realign in the direction due to a torque. The value of torque is :

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Answer: (A) 5×10−9Nm5 \times 10^{-9} \mathrm{Nm}

$\begin{aligned}
& \mathrm{E}=\frac{\mathrm{v}}{\mathrm{~d}}=\frac{5}{5 \times 10^{-4}}=10^4 \mathrm{~V} / \mathrm{m} \\
& \tau=\mathrm{PE} \sin \theta
\end{aligned}$
Where P=qa=2×10−6×5×10−7\mathrm{P}=\mathrm{qa}=2 \times 10^{-6} \times 5 \times 10^{-7}
=1×10−12C−m=1 \times 10^{-12} \mathrm{C}-\mathrm{m}
τ=1×10−12×104×12=5×10−9 N−m\tau=1 \times 10^{-12} \times 10^4 \times \frac{1}{2}=5 \times 10^{-9} \mathrm{~N}-\mathrm{m}

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