What is Electromagnetic Induction?
Electromagnetic induction is the process of generating an electromotive force (EMF) or voltage across a conductor when it is exposed to a changing magnetic field. This phenomenon was discovered by Michael Faraday in 1831 and forms the basis of how we generate electricity today — from massive power plants to the alternator in your car.
The key insight is that a static magnetic field does nothing to a stationary conductor. The field must be changing — either the field strength is varying, the conductor is moving through the field (cutting flux), or the area/angle of the coil exposed to the field is changing.
Faraday's Law of Induction
Faraday's Law states that the induced EMF (ε) is directly proportional to the rate of change of magnetic flux linkage. It depends on:
- N — the number of turns in the coil (more turns = more 'linked' flux).
- ΔΦ — the change in magnetic flux through each turn.
- Δt — the time interval (faster change = higher induced EMF).
Lenz's Law: The Negative Sign
The negative sign in the formula represents Lenz's Law, which is a statement of the conservation of energy. It states that the direction of the induced EMF and current is such that it opposes the change that produced it.
• If you push a North Pole into a coil, the coil becomes a North Pole to repel you.
• If you pull a North Pole out, the coil becomes a South Pole to attract and keep the magnet.
In both cases, you must do work against the magnetic forces, which is where the electrical energy come from!
Three Scenarios for Induced EMF
1. Motional EMF (Moving Rod)
When a straight conductor of length L moves with velocity v perpendicular to a magnetic field B, the electrons inside are pushed to one end by the Lorentz force, creating a potential difference.
2. Rotating Coil (AC Generator)
As a coil rotates at angular velocity ω, the angle of flux changes sinusoidally. The peak EMF occurs when the coil is parallel to the field lines (cutting them most rapidly): ε₀ = NBAω.
3. Changing Field (Transformers)
Even without movement, a changing current in one coil creates a changing magnetic field that induces EMF in a second coil. This is known as mutual induction.
Deep Dive: Worked Examples
✅ Example 1: Moving Rod in a Field
An airplane with a wingspan of 40m flies horizontally at 250 m/s in a region where the Earth's vertical magnetic field component is 5.0 × 10⁻⁵ T. Calculate the EMF induced between the wingtips.
Formula: ε = BLv
Solution:
ε = (5.0 × 10⁻⁵) × 40 × 250
ε = 5.0 × 10⁻⁵ × 10,000 = 0.5 V
✅ Example 2: Faraday's Law for a Coil
A coil of 200 turns is placed in a magnetic field that changes from 0.8 T to 0.2 T in 0.05 seconds. The area of the coil is 0.01 m². Find the average induced EMF.
ΔΦ: ΔΦ = ΔB × A = -0.6 × 0.01 = -0.006 Wb
Formula: ε = -N × (ΔΦ/Δt)
Solution:
ε = -200 × (-0.006 / 0.05) = -200 × (-0.12)
ε = 24 V
✅ Example 3: Peak EMF of a Generator
A small hand-generator has a coil of 50 turns, area 0.005 m², rotating at 600 RPM in a 0.1 T field. Calculate the peak voltage output.
ω: ω = (600 / 60) × 2π = 10 × 2π = 62.83 rad/s
Formula: ε₀ = NBAω
Solution:
ε₀ = 50 × 0.1 × 0.005 × 62.83
ε₀ = 0.025 × 62.83 = 1.57 V
✅ Example 4: Flux Change in a Rotating Coil
A flat coil of radius 10 cm and 100 turns is initially perpendicular to a 0.5 T field. It is rotated by 90° in 0.1 s. Calculate the induced EMF.
Flux Change: Φ₁ = BA = 0.5 × 0.0314 = 0.0157 Wb. Φ₂ = 0 (perpendicular).
ΔΦ: 0 - 0.0157 = -0.0157 Wb
Solution:
ε = -100 × (-0.0157 / 0.1) = -100 × (-0.157)
ε = 15.7 V
✅ Example 5: Energy Conservation
A rod of 0.5m length and 2Ω resistance moves at 10 m/s in a 1.0 T field. Calculate the electrical power dissipated in the rod and the mechanical force required to pull it.
Current: I = ε / R = 5 / 2 = 2.5 A
Electrical Power: P = ε × I = 5 × 2.5 = 12.5 W
Magnetic Force: F = BIL = 1.0 × 2.5 × 0.5 = 1.25 N
Mechanical Power: P = F × v = 1.25 × 10 = 12.5 W (Matches!)