20.5 Electromagnetic induction

Magnetic flux through a surface is Φ=BA cosθ, where θ is the angle between field and the surface normal; units are webers.

Use the component of B perpendicular to the area and state the surface orientation.

A 0.20 T field through 0.50 m² perpendicular surface gives 0.10 Wb.

Flux is not simply B times any projected length, and it is zero when the field lies entirely in the plane of the surface.

When a uniform field is perpendicular to area A, magnetic flux simplifies to Φ=BA.

If the field is tilted, include cosθ; if the area or field varies, integrate or use a suitable average.

Doubling loop area doubles flux at fixed B, while rotating it edge-on reduces perpendicular flux toward zero.

The area is the surface enclosed by the loop, not the wire length.

Flux linkage is NΦ for a coil of N turns when each turn links the same flux; it measures the total linked flux that can induce emf.

Changing turns, field, area or orientation can change linkage. Distinguish flux through one turn from linkage of the whole coil.

A 100-turn coil with 2 mWb per turn has flux linkage 0.20 Wb-turn.

NΦ is not magnetic flux in one turn and does not have the same physical unit interpretation as Φ alone.

When magnetic flux linkage changes, an emf is induced; the induced effect opposes the change according to Lenz’s law.

Change field, area, orientation or motion to change linkage. A complete conducting path is needed for induced current, but emf can exist with an open circuit.

Moving a magnet into a coil gives a transient current whose direction reverses when the magnet is withdrawn.

A static magnetic field alone does not induce emf; it must produce changing flux linkage through the circuit.

Faraday’s law states that induced emf magnitude is the rate of change of flux linkage; Lenz’s law says the induced effect opposes the change causing it.

Change field, area, orientation, turns or motion to change linkage, and use the negative sign as a direction rule.

Moving a magnet faster into a coil produces a larger transient emf; withdrawing it reverses the induced current.

The negative sign does not mean emf is negative in every measurement; it encodes opposition to the change.