Exams › JEE Advanced › Physics

A metal rod of resistance 20 ohm is fixed along a diameter of a conducting ring of radius 0.1 m lying in the xy-plane, in a uniform magnetic field B = 50 T along the z-axis. The ring (with the rod) rotates about its central axis at omega = 20 rad/s. An external resistance of 10 ohm is connected between the ring's centre and its rim. Find the current through the external resistance.

1. 0.33 A
2. 0.50 A
3. 1.0 A
4. 0.25 A

Correct answer: 0.33 A

Solution

Each half of the rod is a radial conductor from centre to rim of length R = 0.1 m, generating emf = (1/2)*B*omega*R² = 0.5*50*20*(0.1)² = 5 V. The rod's 20 ohm splits into two 10 ohm halves; the two halves act as two identical 5 V cells with 10 ohm internal resistance connected in parallel. The parallel combination gives emf 5 V with internal resistance 5 ohm. With the 10 ohm external resistor: I = 5/(5+10) = 1/3 = 0.33 A.

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 →