Exams › JEE Main › Physics

Paragraph: A point charge Q revolves in a circular path of radius R in the x-y plane with angular speed omega. This orbiting charge is equivalent to a current loop carrying steady current Qomega/(2pi). A uniform magnetic field directed along +z is then turned on, growing steadily from 0 to B over a time of one second, while the orbit radius is assumed unchanged. The growing field induces an emf around the orbit (the emf equals the work done by the induced electric field per unit positive charge taken once around the loop). For the orbiting charge, the magnetic dipole moment is proportional to the angular momentum, the constant of proportionality being gamma. The change in the magnetic dipole moment of the orbit at the end of the one-second interval is

1. -gamma*B*Q*R²
2. -gamma*B*Q*R²/2
3. gamma*B*Q*R²/2
4. gamma*B*Q*R²

Correct answer: -gamma*B*Q*R²/2

Solution

The increasing B creates an induced electric field along the orbit. This field tangentially accelerates the charge, changing its angular momentum and therefore (via M = gamma*L) its magnetic moment. Computing the impulse of the induced tangential force gives the change in L, and the sign is negative because the induced effect opposes the change (Lenz's law) for a positive charge in this geometry.

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 →