A dipole comprises two charged particles of identical magnitude q and opposite in nature. The mass m of the positively charged particle is half the mass of the negatively charged particle. The two charges are separated by a distance l. If the dipole is placed in a uniform electric field ⃗E in such…

Question

A dipole comprises two charged particles of identical magnitude q and opposite in nature. The mass m of the positively charged particle is half the mass of the negatively charged particle. The two charges are separated by a distance l. If the dipole is placed in a uniform electric field ⃗E in such a way that the dipole axis makes a very small angle with the electric field ⃗E, the angular frequency of the oscillations of the dipole when released is given by

Accepted Answer

(3) √(4qE)/(3ml). Dipole moment p=ql, so for a small tilt θ the torque is τ=-qlEθ. No external force acts on the pair, so the dipole rotates about its centre of mass. With masses m and 2m a distance l apart, the centre of mass sits (2l)/3 from the lighter charge and l/3 from the heavier one. I_cm=m((2l)/3)²+2m(l/3)²=(4ml²)/9+(2ml²)/9=(2ml²)/3, giving ω=√(qlE)/(2ml²/3)=√(3qE)/(2ml). Take the marked option with care: that correct value is not among the four. Option (c) is what comes out of placing the axis at the geometric centre instead, I=m(l/2)²+2m(l/2)²=(3ml²)/4 and ω=√(4qE)/(3ml), and that is the option the paper keys.

Step-by-step solution

Why the other options are wrong