Electromagnetic Induction

The One Thing

A changing magnetic flux through a circuit produces an induced electromotive force (EMF), whose magnitude is governed by Faraday’s law. The induced effect opposes the change in flux, as stated by Lenz’s law.

Reactions, Processes and Experiments

Key Terms

• Magnetic Flux: The measure of magnetic field passing through a surface, given by Φ = BA cos θ for a uniform magnetic field. Its SI unit is the weber (Wb).
• Electromagnetic Induction: The production of induced EMF in a circuit when the magnetic flux linked with the circuit changes.
• Faraday’s First Law: Whenever the magnetic flux linked with a circuit changes, an induced EMF is produced in the circuit.
• Faraday’s Second Law: The magnitude of induced EMF is equal to the rate of change of magnetic flux linked with the circuit.
• Lenz’s Law: The induced current flows in a direction that opposes the change in magnetic flux responsible for producing it.
• Induced EMF: The potential difference generated due to electromagnetic induction; it can exist even when the circuit is open.
• Motional EMF: EMF produced when a conductor moves through a magnetic field and cuts magnetic field lines.
• Self-Induction: The induction of EMF in a coil due to a change in current through the same coil.
• Self-Inductance: The property of a coil that measures its opposition to changes in current, represented by L.
• Mutual Induction: The induction of EMF in one coil due to a change in current in a nearby coil.
• Mutual Inductance: The ability of one coil to induce EMF in another coil, represented by M.
• Eddy Currents: Circulating currents induced in bulk conductors exposed to changing magnetic flux; they may cause heating and energy loss.
• Back EMF: The self-induced EMF in a coil that opposes a change in current.
• Coefficient of Coupling: The quantity k in M = k√(L₁L₂), with 0 ≤ k ≤ 1, which represents the degree of magnetic coupling between two coils.
• Weber: The SI unit of magnetic flux.
• Henry: The SI unit of inductance. One henry is the inductance that produces an induced EMF of 1 V when current changes at 1 A/s.

Easily Confused

• Electromagnetic induction and magnetic field: A magnetic field alone does not produce an induced EMF; the magnetic flux must change.
• Faraday’s law and Lenz’s law: Faraday’s law determines the magnitude of induced EMF, whereas Lenz’s law determines its direction.
• Self-induction and mutual induction: Self-induction produces an EMF in the same coil whose current changes, whereas mutual induction produces an EMF in a separate nearby coil.
• Self-inductance and mutual inductance: Self-inductance is represented by L for one coil’s opposition to current change; mutual inductance is represented by M for induction between two coils.
• Induced EMF and induced current: An induced EMF can exist in an open circuit, whereas an induced current requires a closed conducting path.
• Motional EMF and transformer-induced EMF: Motional EMF results from a conductor moving through a magnetic field, whereas transformer action results from changing flux linking a coil.
• Useful and unwanted eddy currents: Eddy currents are useful in electromagnetic braking, induction heating, and speedometers, but cause heating and energy loss in transformer cores.

What Gets Asked

• Define magnetic flux and use Φ = BA cos θ, identifying B, A, and θ correctly. A common error is treating θ as the angle between the field and the surface rather than the area normal.
• Apply Faraday’s law using ε = -dΦ/dt, ε = -N(dΦ/dt), or ε_avg = -N(ΔΦ/Δt). Marks are lost if the number of turns N or the negative sign is omitted when it is required.
• Calculate motional EMF using ε = Blv for a conductor moving perpendicular to a magnetic field. The relevant velocity component must be the one that cuts magnetic field lines.
• Determine the direction of induced current using Lenz’s law. The induced effect must oppose the change in magnetic flux, not necessarily oppose the magnetic field itself.
• Distinguish self-induction from mutual induction and use ε = -L(dI/dt) or ε₂ = -M(dI₁/dt) appropriately. A steady current does not induce EMF in a nearby coil if the magnetic flux remains constant.
• Explain applications of electromagnetic induction, including generators, transformers, electromagnetic braking, induction heating, speedometers, and the use of laminated transformer cores to reduce eddy currents.