Physics · Electromagnetic Induction · NEET
The EMF from a rotating coil is ε = NBAω sin(ωt). The full time-varying part is NBAω sin(ωt), and the maximum value of sin is 1. So the biggest EMF the generator ever gives is ε₀ = NBAω. NBA alone is just the maximum flux (Φ₀), not the EMF. The ω appears because EMF is the RATE of change of flux — faster rotation means flux changes faster, so more EMF.
EMF is MAXIMUM when the coil's PLANE is PARALLEL to B (the coil's normal is perpendicular to B). At this instant the flux is zero but it is changing fastest, so EMF peaks. EMF is ZERO when the plane is perpendicular to B (flux is maximum but momentarily not changing). Students often mix these up because 'maximum flux' feels like it should give maximum EMF — but it is the opposite.
Use ω = 2πf, where f is revolutions per second (Hz). If the coil makes 'one revolution per second', f = 1, so ω = 2π rad/s. If given in rpm (revolutions per minute), first divide by 60 to get f in rev/s, then multiply by 2π. Forgetting the 2π is the number-one mistake in these numericals.
Peak EMF ε₀ = NBAω is the highest instantaneous value. RMS EMF is what a voltmeter reads and what carries usable power: ε_rms = ε₀/√2 ≈ 0.707 ε₀. NEET numericals on the generator almost always ask for PEAK (maximum) EMF or peak current. Read the word 'maximum' carefully — if it just says 'the EMF read by a meter' or 'rms', divide by √2.
Peak current I₀ = ε₀/R = NBAω/R, where R is the coil's resistance. First compute ε₀ = NBAω, then divide by R. This is exactly what NEET 2022 tested: it gave N, B, radius, ω and R, and asked for maximum induced current.
An emf is generated by an AC generator having a 100-turn coil of loop area 1 m². The coil rotates at one revolution per second in a uniform magnetic field of 0.05 T perpendicular to the axis of rotation. The maximum value of emf is:
A big circular coil of 1000 turns and average radius 10 m rotates about its horizontal diameter at 2 rad s⁻¹. If the vertical component of earth's magnetic field is 2 × 10⁻⁵ T and the coil's resistance is 12.56 Ω, the maximum induced current in the coil will be:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
ε₀ = NBAω, where N is the number of turns, B is the magnetic field in tesla, A is the coil area in m², and ω is the angular speed in rad/s. The full EMF is ε = ε₀ sin(ωt).
N is a pure number (turns), B is in tesla (T), A is in square metres (m²), and ω is in radians per second (rad/s). The result ε₀ comes out in volts (V).
No. Peak EMF depends only on N, B, A and ω. Resistance R only matters when you find the peak CURRENT: I₀ = ε₀/R = NBAω/R.
EMF is the rate of change of flux. A larger ω means the flux through the coil changes more quickly, so a bigger EMF is induced. That is why ω multiplies inside ε₀ = NBAω.
NEET generator numericals almost always ask for the maximum (peak) EMF ε₀ = NBAω or the peak current. If the question specifically says 'rms', divide the peak value by √2.
