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Physics Question 37 – JEE-MAIN 2025

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A dipole with two electric charges of 2 μC magnitude each, with separation distance 0.5 μm, 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∘ from the axis, it tends to realign in the direction due to a torque. The value of torque is :

Recall the definitions of electric dipole moment and electric field in a capacitor, and the formula for torque on a dipole.

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Ninja Strategy•Order of Magnitude Estimation

Estimate the order of magnitude of the dipole moment (p) and electric field (E) first. The product pE will give a rough idea of the torque's magnitude, allowing elimination of options that are orders of magnitude off.

Step 1: Calculate Electric Dipole Moment and Electric Field✦ Active

First, calculate the electric dipole moment (p) using the charge magnitude (q) and separation distance (d), and the electric field (E) between the capacitor plates using the potential difference (V) and plate separation (D). Ensure all values are in SI units.

q=2 μC=2×10−6 C d=0.5 μm=0.5×10−6 m p=qd=(2×10−6 C)×(0.5×10−6 m)=1×10−12 C m V=5 V D=0.5 mm=0.5×10−3 m E=VD=5 V0.5×10−3 m=10×103 V/m=104 N/C
Step 2: Calculate Torque on the Dipole○ Expand

Now, use the formula for torque (τ) on an electric dipole in a uniform electric field, which is τ=pEsin⁡θ, where θ is the angle between the dipole moment and the electric field.

θ=30∘⟹sin⁡θ=sin⁡(30∘)=0.5 τ=pEsin⁡θ=(1×10−12 C m)×(104 N/C)×0.5 τ=0.5×10−8 Nm=5×10−9 Nm
💡 Teacher's Secret Hint

Double-check your unit conversions and the value of sin⁡(30∘).

Step 3: Match with Options○ Expand

The calculated torque is 5×10−9 Nm, which corresponds to option 2.

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