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A dipole made of two charges of magnitude 2 μC each, separated by 0.5 μm, is placed between the plates of a capacitor with its axis parallel to the field set up when a potential difference of 5 V is applied. The separation between the plates is 0.5 mm. If the dipole is rotated by 30° from the axis, it tends to realign with the field because of a torque. The value of the torque is

Asked in JEE Main 7th April 2nd Shift 2025 · Torque, energy and work done

• (1) 5×10⁻³ N m
• (2) 2.5×10⁻⁹ N m
• (3) 2.5×10⁻¹² N m
• (4) 5×10⁻⁹ N m

Step-by-step solution

Why the other options are wrong

• (1) Reads the dipole separation as 0.5 m instead of 0.5 μm, losing the factor 10⁻⁶ in p.
• (2) Takes sin 30°=1/4, or equivalently halves the answer a second time after already applying sin 30°.
• (3) Takes the field as the bare potential E=5, never dividing by the plate separation, so τ=10⁻¹²×5×sin 30°=2.5×10⁻¹² N m.

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