Exams › JEE Main › Physics
Two long parallel straight wires lie on a frictionless table, and two more parallel wires rest across them at right angles, initially forming a square of side a. A uniform magnetic field B is perpendicular to the plane of the wires. All four wires begin moving outward with constant speed v. If r is the resistance per unit length of the wire, what current flows in the circuit?
- Bv/r
- Br/v
- Bvr
- Bv
Correct answer: Bv/r
Solution
Let the side be s. Each pair of opposite wires separates at relative speed 2v, but treating the standard result: emf = B*dA/dt. With area A = s² and ds/dt giving dA/dt, and the loop resistance = r*(perimeter) = r*4s, the s-dependence cancels and the current becomes independent of size, equal to Bv/r. This is the classic result for such an expanding square.
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 →