Rotating Coil and AC Generator
For a coil of N turns and area A rotating at angular speed omega in uniform B, the peak emf is N B A omega.
Why this shows up in the exam
Power-station alternators · Bicycle dynamos · Turbine generators
Learn the idea
A rotating coil converts mechanical rotation into sinusoidal emf. Rotation continuously changes the angle between the coil's area vector and magnetic field. The flux is cosine-shaped, so its time derivative, the emf, is sine-shaped.
🧠 Memory hook: Flux is cosine; emf is its derivative sine.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Phi = N B A cos(omega t) — flux linkage of a rotating coil
- emf = N B A omega sin(omega t) — generated emf
- emf₀ = N B A omega — peak emf
How to approach it
- 1Write flux first
- 2Differentiate
- 3Check the quarter-cycle phase difference
Common slip-ups that cost marks
- •Confusing angular speed with frequency
- •Forgetting N
- •Assuming maximum flux and maximum emf occur together
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A conducting rod of length 2 m moves at 3 m/s perpendicular to a 4 T magnetic field. Find the motional emf.
More from Electromagnetic Induction and Alternating Currents
AC Circuit Analysis and LCR Circuits
AC circuits with resistors, capacitors, and inductors (LCR circuits) exhibit impedance, resonance, phase relationships, and power factor, all crucial for understanding circuit behavior.
AC Generators and Transformers
AC generators convert mechanical energy to electrical energy using electromagnetic induction, while transformers transfer electrical energy between circuits, often changing voltage levels.
Faraday's Law and Lenz's Law
Faraday's law explains how a changing magnetic field induces an electromotive force (EMF), while Lenz's law determines the direction of the induced current to oppose the change causing it.
Self and Mutual Inductance
Self-inductance is the property of a coil to oppose changes in its own current, while mutual inductance is the ability of one coil to induce EMF in another nearby coil.
Eddy Currents and Applications
Eddy currents are circulating currents induced in conductors by changing magnetic fields, leading to energy loss and effects like electromagnetic damping.
Motional EMF
Motional EMF is the voltage induced in a conductor moving through a magnetic field, depending on the speed, length, and orientation of the conductor.