What is Electromagnetic Induction?
💡 In Simple Words: When a magnetic field around a coil changes, the coil creates a voltage on its own. That voltage makes current flow if you close the loop – just like water starts moving when you tilt a pipe.
Electromagnetic induction (EMI) is the process of generating an electromotive force (emf) – a fancy word for voltage – by changing magnetic flux. Magnetic flux is the amount of magnetic field passing through an area, kind of like how many raindrops fall on a roof.
Two rules govern EMI:
- Faraday's law says the induced emf equals the rate at which magnetic flux changes. In symbols, ε = -dΦ/dt. The minus sign is Lenz's law.
- Lenz's law tells us the direction of the induced emf opposes the change that created it. It’s the electrical version of “if you push a swing, it pushes back.”
How an AC Circuit Uses Induction
AC stands for alternating current – the current flips direction many times a second. A simple AC generator is a coil that spins inside a magnet. Spinning changes the magnetic flux, so Faraday’s law produces an alternating emf. That emf drives the AC current through the external circuit.
Key parts of an AC circuit:
- Self‑inductance (L): a coil’s own changing current creates a magnetic field that tries to keep the current steady. Think of it as a spring that resists sudden motion.
- Mutual inductance (M): when two coils sit near each other, the changing current in one induces emf in the other. This is how a transformer works.
- RMS value (root‑mean‑square): a way to compare AC voltage to a DC voltage that would give the same heating effect. For a sine wave, RMS = peak/√2.
Worked Example: Finding Induced emf
Imagine a rectangular coil of 50 turns, each side 0.1 m, placed in a uniform magnetic field of 0.2 T. The field direction is perpendicular to the coil, but the coil rotates at 60 rev/s. What is the maximum emf?
Step‑by‑step:
- Calculate angular speed ω = 2π × 60 ≈ 376 rad/s.
- Magnetic flux Φ = B A cosθ, where A = (0.1 m)² = 0.01 m².
- Maximum change occurs when cosθ varies fastest, i.e., at sinθ = 1. So |dΦ/dt|_max = B A ω.
- Plug numbers: B A ω = 0.2 × 0.01 × 376 ≈ 0.752 Wb/s.
- Induced emf ε_max = N |dΦ/dt|_max = 50 × 0.752 ≈ 37.6 V.
So the coil can generate about 38 V peak alternating voltage.
Self‑Inductance vs Mutual‑Inductance: Quick Comparison
| Feature | Self‑Inductance (L) | Mutual Inductance (M) |
|---|---|---|
| What creates the emf? | Changing current in the same coil | Changing current in a nearby coil |
| Typical symbol | L (henry) | M (henry) |
| Formula | ε = -L di/dt | ε₂ = -M di₁/dt |
| Used in | RL circuits, inductors | Transformers, coupled coils |
Induction Process Flowchart
Common Mistakes to Avoid
- Forgetting the negative sign in Faraday’s law – it tells you the direction, not the magnitude.
- Mixing up peak and RMS values; always convert when comparing AC to DC.
- Assuming a coil with no resistance has no power loss – the magnetic field still stores energy, which later shows up as heat.
📝 Likely Exam Questions
- State Faraday’s law and explain Lenz’s law with an example.
Answer: Faraday’s law says the induced emf equals the rate of change of magnetic flux (ε = -dΦ/dt). Lenz’s law gives the minus sign – the induced emf opposes the flux change. Example: When a magnet is pushed into a coil, the coil produces a current that creates a magnetic field repelling the magnet. - A coil of 200 turns rotates at 50 rev/s in a 0.1 T field. Find the peak induced emf if the coil area is 0.02 m².
Answer: ω = 2π × 50 = 314 rad/s. Φ_max = B A = 0.1 × 0.02 = 0.002 Wb. ε_max = N B A ω = 200 × 0.1 × 0.02 × 314 ≈ 125.6 V. - Differentiate between self‑inductance and mutual inductance.
Answer: Self‑inductance is the emf induced in a coil by its own changing current (ε = -L di/dt). Mutual inductance is the emf induced in one coil by the changing current in a neighboring coil (ε₂ = -M di₁/dt). L depends on the coil’s geometry; M depends on the coupling between two coils. - Explain why the RMS value of a sinusoidal AC voltage is lower than its peak value.
Answer: RMS is the square root of the average of the squared instantaneous values over a cycle. For a sine wave, this works out to peak/√2, because the voltage spends part of the time below its peak, reducing the average heating effect.