Electromagnetic Induction (AP Physics 2 Unit 4) — Concepts, Laws, and Real Devices

Magnetic flux (Φ_B)

A measure of how much magnetic field passes through a chosen surface; for a uniform field through a flat area: Φ_B = BA cos(θ).

Weber (Wb)

The SI unit of magnetic flux (Φ_B).

Area vector

A vector perpendicular to a surface whose direction you choose; it sets the sign convention for magnetic flux through that surface.

Effective area (A cos θ)

The portion of a surface area that is “seen” by the magnetic field in flux calculations; equals A cos(θ), where θ is between B and the area vector.

Faraday’s law of induction

The induced emf in a loop/coil equals the negative rate of change of magnetic flux: ℰ = −N(dΦ_B/dt).

Lenz’s law

The induced current flows so that the magnetic field it produces opposes the change in magnetic flux (the negative sign in Faraday’s law).

Electromotive force (emf, ℰ)

Energy per charge provided by a source that drives charge around a circuit (units: volts); in induction, it comes from changing magnetic flux.

Number of turns (N)

The number of identical loops in a coil; induced emf scales with N because each turn experiences the same flux change (ℰ = −N dΦ_B/dt).

Average induced emf (ℰ_avg)

A form of Faraday’s law used over a time interval when change is approximately uniform: ℰavg = −N(ΔΦB/Δt).

Right-hand rule for a current loop

Curl fingers in the direction of conventional current; thumb points in the direction of the loop’s magnetic field through the loop.

Motional emf

An emf produced by moving a conductor through a magnetic field; for a rod of length ℓ moving at speed v perpendicular to B: ℰ = Bℓv (more generally ℰ = Bℓv sin θ).

Flux linkage (NΦ_B = LI)

Relationship showing that current in a coil produces magnetic flux; the proportionality constant is the inductance L.

Inductance (L)

A measure of how strongly a circuit element (usually a coil) opposes changes in current by inducing an emf; appears in ℰ = −L(dI/dt).

Henry (H)

The SI unit of inductance L.

Self-induction

Induction in which a circuit’s changing current changes its own magnetic flux, producing an induced emf that opposes the current change.

Energy stored in an inductor

Energy stored in the magnetic field of an inductor: U = (1/2)LI^2.

RL time constant (τ)

The timescale for current to change in a series RL circuit: τ = L/R; current cannot change instantly because the inductor induces an opposing emf.

Eddy currents

Loops of induced current in a bulk conductor caused by changing magnetic flux; can cause heating losses or be used for damping/braking.

Magnetic braking

Using induced currents (often eddy currents) whose magnetic fields oppose motion, producing a force that slows an object (Lenz’s law).

Electric generator

A device that produces emf by rotating a coil in a magnetic field, changing θ in Φ_B = BA cos θ and inducing a (typically AC) voltage.

Transformer

A device that uses changing magnetic flux in a core to induce voltages in primary and secondary coils, changing AC voltage levels.

Ideal transformer voltage ratio

For an ideal transformer, secondary-to-primary voltage ratio equals turns ratio: Vs/Vp = Ns/Np.

Ideal transformer power conservation

In an ideal transformer, input power equals output power: Pp = Ps (so higher voltage corresponds to lower current and vice versa).

Step-up transformer

A transformer with Ns > Np that increases voltage and decreases current on the secondary side (ideal case).

Resistive transmission loss (P_loss = I^2R)

Power lost as heat in transmission wires; reducing current I (often by using high voltage) greatly reduces losses because loss scales with I^2.