Electromagnetic Induction

Lesson

Part 1 — how a changing magnetic flux produces an emf, how big it is, and which way the induced current flows.

In this lesson you will

Define magnetic flux and state Faraday’s laws of electromagnetic induction
Calculate the induced emf from a changing flux
Use Lenz’s law to find the direction of an induced current, and relate it to conservation of energy

Concept

Faraday’s experiments

A coil connected to a galvanometer shows a current only while something is changing:

A magnet moved towards or away from the coil (faster motion, bigger deflection; reversing the motion reverses the current).
The coil moved near a stationary magnet: only relative motion matters.
The current in a nearby coil switched on or off, or varied.

Table of Faraday’s observations: no deflection with a still magnet, opposite deflections for pushing in and pulling out, brief kicks when a nearby circuit is switched
Action	Galvanometer
Magnet held still in the coil	No deflection
N pole pushed in	Deflects one way
N pole pulled out	Deflects the other way
Nearby circuit switched on / off	Brief kicks in opposite directions

Concept

Magnetic flux

The magnetic flux through a plane area $A$ in a uniform field $B$ is $\Phi_B = \vec B\cdot\vec A = BA\cos\theta$ where $\theta$ is the angle between $\vec B$ and the normal to the area. SI unit: weber (Wb) $= 1$ T m². For $N$ turns the flux linkage is $N\Phi_B$ .

Flux can change by changing $B$ , the area $A$ , or the angle $\theta$ .
For a non-uniform field: $\Phi_B = \int \vec B\cdot d\vec A$ .

Table of flux for a coil face-on, tilted and edge-on to the field
Orientation of the coil	θ	Flux
Face-on to B	0°	BA (largest)
Tilted	θ	BA cos θ
Edge-on to B	90°	0

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