A dipole comprises two charges +q and −q separated by distance l. The mass m of the positive charge is half the mass of the negative charge. The dipole is placed in a uniform electric field E with its axis making a very small angle with the field. The angular frequency of small oscillations is:
Physics · Circular Motion
JEE Mains 6 April 2023 Shift 2 Evening Shift

Question

A dipole comprises two charges +q and −q separated by distance l. The mass m of the positive charge is half the mass of the negative charge. The dipole is placed in a uniform electric field E with its axis making a very small angle with the field. The angular frequency of small oscillations is:

Physics · Circular Motion

JEE Mains 6 April 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

Let the positive charge +q have mass m and the negative charge −q have mass 2m. Their separation is l. For rotation about the centre of mass, the moment of inertia is I = μ(red) l² where the reduced mass is μ(red) = (m×2m)/(m+2m) = 2m/3 Thus, I = (2/3)ml² For a small angular displacement θ in a uniform electric field, τ ≈ −pEθ = −q l E θ Hence, I(d²θ/dt²) = −q l E θ So, ω² = qlE/I = qlE / [(2/3)ml²] = 3qE/(2ml) Therefore, ω = √[3qE/(2ml)] The source solution notes that this result does not exac…