A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :

Solution

Physics sir · 3 steps

Flux is largest when emf is zero: write flux as a cosine and the emf comes out as a sine.

1. Write the flux. At t = 0 the plane is perpendicular to B⃗, so the area vector is along B⃗ and the flux is maximum. As the loop turns, φ = BA cos ω t with ω = 2π/T = 2π/10 rad s⁻¹.

   ε = -dφ/dt = BAω sin((2π t)/10)

2. Check each time. At t = 2.5 s the angle is π/2, so |sin| = 1 and the emf is maximum. At t = 5 s the angle is π, so sin = 0 and the emf is minimum (zero). The emf is also maximum at 7.5 s and zero at 10 s.
3. So. The first maximum and the first minimum after the start come at 2.5 s and 5.0 s, which is option (d).

The idea to keep. In a rotating loop, emf follows the rate of change of flux, not the flux itself. When the flux peaks, the emf is zero. A quarter turn later the flux is zero and the emf peaks.

Answer from the NTA final answer key. Solution by PrepWiser.