Electromagnetic Induction

Lesson

Part 1 — a changing magnetic flux drives a current: Faraday’s and Lenz’s laws, motional emf and eddy currents.

In this lesson you will

Calculate magnetic flux and use Faraday’s laws to find induced emf, current and charge
Apply Lenz’s law and relate it to conservation of energy; derive E = Blv and the power (Blv)²/R
Explain the causes, effects and uses of eddy currents

Concept

Magnetic flux

For a flat coil of area $A$ in a uniform field $B$ , the magnetic flux through it is $\Phi = \vec B \cdot \vec A = BA\cos\theta$ where $\theta$ is the angle between $\vec B$ and the normal to the coil. Unit: weber (1 Wb = 1 T m²). For $N$ turns the flux linkage is $N\Phi$ .

Largest (BA) when the plane of the coil is perpendicular to B; zero when the plane is parallel to B.
Careful: an angle given between the field and the PLANE of the coil must be changed to 90° minus that angle.

Concept

Faraday’s laws of electromagnetic induction

First law: whenever the magnetic flux linked with a circuit changes, an emf is induced in it; it lasts only while the change continues. Second law: the induced emf equals the rate of change of flux linkage: $\varepsilon = -N\,\dfrac{d\Phi}{dt}$

The flux can change through B, through A or through the angle θ.
The minus sign is Lenz’s law (next slides). Induced current $I = \varepsilon/R$ .

Table of Faraday’s observations: a galvanometer connected to a coil deflects only while the flux through the coil is changing, more for a faster change, and in opposite directions for opposite changes
What is done	Galvanometer
Magnet pushed into the coil	deflects one way
Magnet held still inside the coil	no deflection
Magnet pulled out	deflects the other way
Magnet moved faster	larger deflection
Current switched on in a nearby coil	brief kick

Cookies