Exams › JEE Main › Physics
A non-conducting ring of mass m, radius r and total charge Q rests on a rough horizontal surface in a region of perpendicular (transverse) magnetic field whose magnitude increases with time at the rate R (dB/dt = R). If mu is the coefficient of friction between the ring and the surface, find the minimum mu required for the ring to stay in rotational equilibrium (not start rotating).
- Q*r*R/(2*m*g)
- Q*r*R/(m*g)
- Q*r*R/(3*m*g)
- 2*Q*r*R/(m*g)
Correct answer: Q*r*R/(2*m*g)
Solution
The increasing field induces a circulating electric field E = (r/2)*(dB/dt) = (r/2)*R along the ring. The force on the ring's charge is Q*E, giving a driving torque tau_drive = Q*E*r = Q*(r/2)*R*r = Q*R*r²/2. The maximum static friction torque available is tau_fric = mu*N*r = mu*m*g*r (friction acts at radius r). For equilibrium tau_fric >= tau_drive: mu*m*g*r >= Q*R*r²/2, so mu >= Q*r*R/(2*m*g).
Related JEE Main Physics questions
- A metallic ring is kept in a horizontal position, and a bar magnet is released so that it falls through the ring with its length aligned along the ring’s axis. The magnet’s acceleration while falling is
- A coil has resistance 10 Ω, and the magnetic flux linked with it changes with time according to ϕ = 4t² + 2t + 1 (in weber). The current induced in the coil at t = 1 s is
- Two coils are kept near one another. The mutual inductance of the coil pair depends on
- A conducting rod of length ℓ is attached to a string of length 2ℓ and is rotated on a horizontal table about the fixed end of the string with angular speed ω. If a uniform magnetic field B acts vertically through the region, what is the induced emf between the two ends of the rod?
- A pair of coils, each having N turns, has mutual inductance M henry. If the current in one coil changes from 1 ampere to zero in time t seconds, what is the induced emf per turn in the other coil, in volts?
- A boat travels straight toward the east in a place where Earth’s magnetic field is horizontal, points due north, and has magnitude 5.0 × 10⁻⁵ N A⁻¹ m⁻¹. A 2 m long vertical antenna is mounted on the boat. If the boat’s speed is 1.50 m s⁻¹, what emf is induced across the antenna wire?
⚔️ Practice JEE Main Physics free + battle 1v1 →