Exams › JEE Advanced › Physics

A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface (acting as a long solenoid-like sheet). A wire loop of resistance 0.005 ohm and radius 0.1 m is placed coaxially inside the tube. The current varies as I = I0*cos(300t). If the induced magnetic moment of the loop is N*mu0*I0*sin(300t), find N.

1. 6
2. 3
3. 12
4. 1

Correct answer: 6

Solution

Field inside the tube: B = mu0*(I/L) (single current sheet of length L carrying total I, treated as n = 1/L turns per metre). Flux through loop: phi = B*pi*r² = mu0*(I/L)*pi*r². emf = -dphi/dt = mu0*(pi*r²/L)*I0*300*sin(300t). Induced current i = emf/Res. Magnetic moment m = i*pi*r² = (mu0*pi²*r⁴*300/(L*Res))*I0*sin(300t). Plug r = 0.1, L = 10, Res = 0.005: pi²*r⁴ = pi²*1e-4; factor = mu0*I0*sin(300t)*(pi²*1e-4*300/(10*0.005)) = mu0*I0*sin(300t)*(pi²*1e-4*300/0.05) = mu0*I0*sin(300t)*(pi²*0.6) approx mu0*I0*sin(300t)*5.92, so N approx 6.

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 →