Exams › JEE Advanced › Physics

A circular loop of radius r spins about the z-axis with angular velocity omega; its normal stays perpendicular to z (in the x-y plane). At t = 0 the normal points along +y. A constant external field B = B_y j + B_z k is present. What is the induced EMF, epsilon(t), in the loop?

1. pi r² omega B_y sin(omega t)
2. pi r² omega B_z cos(omega t)
3. pi r² omega B_z sin(omega t)
4. pi r² omega B_y cos(omega t)

Correct answer: pi r² omega B_y sin(omega t)

Solution

The normal rotates in the x-y plane: n = cos(omega t) j - sin(omega t) i (starting along +y). Flux Phi = (pi r²)(B. n) = pi r² B_y cos(omega t) (B_z k contributes nothing since n has no z-component). EMF = -dPhi/dt = pi r² omega B_y sin(omega t).

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 →