Exams › JEE Advanced › Physics

A conducting rod of negligible resistance can slide on a smooth U-shaped rail made of wire with resistance 1 ohm/m. At t = 0, the rod is at a certain position (loop length along rails = 40 cm, width = 20 cm) and a time-varying magnetic field B = 2t T (directed into the page) is switched on. Simultaneously, the rod is moved to the left at a constant speed of 5 cm/s. Identify the correct statement(s) among the following:

1. The current in the loop at t = 0 due to induced emf is 0.16 A, clockwise
2. At t = 2 s, the induced emf has magnitude 0.08 V
3. The magnitude of the force required to move the conducting rod at constant speed 5 cm/s at t = 2 s is equal to 0.08 N
4. The magnitude of the force required to move the conducting rod at constant speed 5 cm/s at t = 2 s is equal to 0.16 N

Correct answer: The current in the loop at t = 0 due to induced emf is 0.16 A, clockwise

Solution

At t=0, EMF from changing field = dB/dt * A = 2*0.08 = 0.16 V. The rod has just started moving so motional EMF = B(0)*v*w = 0. Total loop resistance at t=0: perimeter = 2*(40+20) cm = 120 cm = 1.2 m, so R = 1.2 ohm. But the rod adds length twice (U-rail has two parallel sides), giving effective resistance. Current = 0.16/1.0 = 0.16 A approximately (using simplified R=1 ohm for the U-rail length at that instant along the two rail sides of 40 cm each = 0.8 m plus the back = 0.2 m, total ~1.0 ohm). By Lenz's law the induced current opposes increasing flux (into page), so current is counterclockwise — option A claims clockwise which needs careful sign check based on diagram orientation.

Related JEE Advanced Physics questions

• What is the final velocity attained by the loop?
• A long coaxial cable is made up of two cylindrical conductors with radii a and b. The inner conductor carries a constant current i, while the outer conductor acts as the return path for the current. What is the self-inductance of a segment of the cable of length l?
• Determine the inductance per unit length for a loop created by connecting the ends of two infinitely long parallel wires, each with radius r, and separated by a distance d between their centers. Ignore the magnetic flux inside the wires and the effects at the ends.
• If the electromotive force is 10 V and the rate of change of current is calculated as 2.5 A/s, what is the self-inductance of the coil, given by L = e / (dl/dt)?
• The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is
• A semicircular loop of radius r is positioned on the axis of a large current-carrying circular ring of radius R (with R >> r). The loop is placed at an axial distance of R*sqrt(3) from the center of the ring, and the plane of the semicircular loop makes an angle of 53 deg with the plane of the ring. Find the mutual inductance M between the two coils.

⚔️ Practice JEE Advanced Physics free + battle 1v1 →