Summary Electromagnetic Induction Physics A-Level

Electromagnetic induction
Specification

(a) recall and define magnetic flux as ABcosand flux linkage = N
(b) recall the laws of Faraday and Lenz,
(c) recall and use e.m.f. = – rate of change of flux linkage and use this relationship to derive
an equation for the e.m.f. induced in a linear conductor moving at right angles to a uniform
magnetic field,
(e) relate qualitatively the instantaneous e.m.f. induced in a coil rotating at right angles to a
magnetic field to the position of the coil, flux density, coil area and angular velocity;

Magnetic flux

 Magnetic flux (Φ) = ABcos where A is the area (A will nearly always be the area of
some sort of a loop of wire and won’t be related to an imaginary surface), B is the B-
field and is the angle between the normal to the surface and the B-field (i.e. the
field lines). Unit = Weber, Wb (or Tm2).
 When the surface and B are at an angle, we resolve the field to get the component
perpendicular to the surface (hence Bcos) i.e. only the perpendicular component of
the magnetic field contributes to magnetic flux. However in many cases, the field
lines will be parallel to the normal of the surface and so the equation can be simplified
to Φ = AB.
 The magnetic flux through a given surface is related to the number of magnetic field
lines that pass through the surface. This explains why we take the perpendicular
component of the magnetic field (as the parallel component does not pass through A).
 By rearranging the equation, B = Φ/A (and taking  = 0) we see that the magnetic flux
density is the magnetic flux per unit area, hence the wording magnetic flux density.
This shows that magnetic flux density is related to the number of field lines passing
through A per unit area.

Flux linkage

 However in many cases, we often have many loops (turns) in a conductor e.g. a
solenoid. In this case, field lines are passing through multiple A’s and so the flux
through the conductor is larger.
 If a coil has N loops and the magnetic flux through each loop is Φ then the total
magnetic flux for all loops is: total magnetic flux for the whole of the coil = flux
linkage = NΦ (use this as symbol).
 Most of the time you will be able to write: flux linkage = NΦ = BAN because cos =
1 and the same flux passes through each of the N loops. Unit = Wb-turn.

Faraday’s law

 Faraday’s law = the induced EMF is equal to the rate of change of the magnetic flux
linkage. V = – Δ(BAN)/Δt where BAN is the flux linkage. NB this equation assumes
cos = 1 which will be the case for A-level calculations that need to be done.
 You should realise that there are two ways of inducing an EMF from Faraday’s law:
varying the B-field or varying the area (through some sort of motion).

,  NB can use alternative version of Faraday’s law: the induced EMF is equal to the rate
of flux cutting (i.e. in terms of magnetic flux lines being cut).

Induced current or EMF?

 If you move a conductor through a magnetic field, you always induce an EMF. If
there is a circuit available, the EMF will push a current through it. If there is no
circuit you will still get an EMF, but you won't get a current.
 So if the secondary coil in a transformer is not a circuit, there will not be an induced
current.

Application: moving a bar magnet in and out of a coil of wire




 NB think of gradient of B-t graph.
 When the magnetic moves into the coil of wire, an EMF is induced in one direction
because there is ΔB/Δt.
 When the magnet is stationary, the EMF is 0 because ΔB/Δt = 0.
 When the magnetic moves out of the coil, an EMF is induced in the other direction.
 NB The flux first increases (ΔB/Δt > 0) and then decreases (ΔB/Δt < 0), so the
direction of the EMF changes.

Application: transformer

This can be used to explain how an alternating EMF is induced in a transformer: