Electromagnetic Induction is the phenomenon of producing an EMF (and hence current) in a conductor by changing the magnetic flux through it. Discovered by Michael Faraday in 1831, it is the basis of electric generators and transformers.
Key Concepts
- Magnetic Flux: phi = B · A cos(theta), where theta is the angle between the magnetic field B and the area vector (normal to the surface). Unit: Weber (Wb = T·m2).
- Faraday's First Law: An EMF is induced in a circuit whenever the magnetic flux through it changes.
- Faraday's Second Law: The magnitude of the induced EMF is directly proportional to the rate of change of flux: epsilon = -d(phi)/dt.
- Lenz's Law: The direction of the induced current is such that it opposes the change in flux that caused it. This is a consequence of conservation of energy. The negative sign in Faraday's law represents Lenz's Law.
- Motional EMF: When a conductor of length L moves with velocity v perpendicular to a magnetic field B, the EMF induced is epsilon = BLv. Current = BLv/R if connected in a circuit.
- Eddy Currents: When a bulk conductor is placed in a changing magnetic field, circulating currents (eddy currents) are induced inside it. They produce heat (energy loss). Minimised by using laminated cores.
- Self-Inductance (L): When the current in a coil changes, the flux through the coil changes and an EMF is induced in the same coil. epsilon = -L × dI/dt. L depends on coil geometry; unit is Henry (H).
- Self-inductance of a solenoid: L = µ0 n2 A l, where n = turns per unit length, A = area, l = length.
- Mutual Inductance (M): An EMF is induced in coil 2 due to changing current in coil 1. epsilon2 = -M × dI1/dt. M depends on geometry and relative position of coils.
- Energy stored in an inductor: U = LI2 / 2.
- Key Formulas
- epsilon = -N d(phi)/dt = -N d(BA cos theta)/dt
- Motional EMF: epsilon = BLv
- Self-inductance of solenoid: L = µ0 n2 V (V = volume = A × l)
- Energy in inductor: U = LI2/2
---
A coil of 200 turns has a flux that changes from 0.05 Wb to 0.03 Wb in 0.1 s. Find the induced EMF.
epsilon = -N × delta(phi)/delta(t) = -200 × (0.03 - 0.05)/0.1 = -200 × (-0.2) = 40 V
A straight conductor 0.5 m long moves at 4 m/s perpendicular to a field B = 0.3 T. Find the motional EMF.
epsilon = BLv = 0.3 × 0.5 × 4 = 0.6 V
State and explain Lenz's Law using a falling magnet over a coil.
As the north pole of a magnet approaches the top of a coil, the flux through the coil increases. By Lenz's law, the induced current flows such that it creates a north pole at the top of the coil (opposing the approaching north pole). When the magnet recedes, the induced current reverses to create a south pole (attracting the departing north pole). In both cases, the induced current opposes the change.
A solenoid has 500 turns, length 0.5 m, cross-section area 4 × 10-4 m2. Find its self-inductance.
n = 500/0.5 = 1000 turns/m
L = µ0 n2 A l = 4 pi × 10-7 × 106 × 4 × 10-4 × 0.5 = 4 pi × 10-7 × 4 × 102 × 0.5 = 4 pi × 10-7 × 200 = 2.51 × 10-4 H
The current in a coil changes from 2 A to 5 A in 0.1 s. If the induced EMF is 30 V, find the self-inductance.
epsilon = L × dI/dt => 30 = L × (5 - 2)/0.1 = L × 30 => L = 1 H
Explain why eddy current losses are reduced by using laminated cores in transformers.
Eddy currents circulate in closed loops in the plane perpendicular to B. Laminated cores (thin insulated sheets) break these loops into smaller paths, dramatically increasing resistance and reducing eddy current magnitude and hence power loss (P = I2 R with smaller I).
The mutual inductance between two coils is 0.5 H. The current in the primary changes at 4 A/s. Find the EMF in the secondary.
epsilon2 = M × dI1/dt = 0.5 × 4 = 2 V
---
Common mistakes
- The negative sign in Faraday's law (Lenz's law) is often dropped. Remember: it tells you the direction of induced EMF opposes the cause.
- Self-inductance L depends on the geometry of the coil and the medium — NOT on the current in it.
- Do not confuse magnetic flux (phi = BA cos theta) with flux linkage (N × phi).
Summary
Electromagnetic induction, described by Faraday's and Lenz's laws, is the basis of electrical energy generation. Key ideas include magnetic flux, induced EMF, motional EMF, eddy currents, self-inductance, and mutual inductance — all essential for understanding AC generators and transformers.