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Magnetic field patterns


More magnetic field patterns


The motor effect


Fleming’s left-hand rule

The direction of the force acting on a wire carrying a current can be predicted using Fleming’s left-hand rule.

thuMb = Motion

First finger = magnetic Field (N to S)

seCond finger = Current

The current is in the direction of moving positive charge.


Measuring the force on a conductor

What factors affect the force on a conductor in a magnetic field? How could they be investigated?

ammeter

rheostat

By varying the current with the rheostat and using different length conductors, you could see how the downforce varies.

conductor

balance

non-conducting support


Magnetic flux density

Magnetic flux density, B, is the force per unit current per unit length, on a current-carrying wire in a magnetic field.It is the ‘strength’ of a magnetic field.

The unit of magnetic flux density is the tesla (T).One tesla is equal to 1 N m-1

A-1.

F = BILsinθ

Rearranging: B = F / ILsinθ

×force =magnetic

flux densitycurrent

length of wire in

field

sine of angle between wire

and field× ×


Force on a wire calculations


Magnetic fields: true or false?


Electron deflection


The force on a moving charge

Consider a particle with positive charge Q moving at velocity v at right angles to a magnetic field of magnetic flux density B:

In time t the particle will have a current I, given by I = Q/t. The particle will also travel a distance L, given by L = vt.

Substituting into F = BIL gives:

F = B × Q/t × vt which simplifies to: F = BQv

Using Fleming’s left-hand rule, if the charge in the diagram is positive, the direction of the force will be into the screen.


Moving charges calculations


Charges not moving at 90° to the field

What happens if the charge does not move at right angles to the field, but at an angle θ?

The horizontal component of the velocity, vcosθ, is parallel to the field and can be discounted.

The perpendicular component of the velocity is given by vsinθ.

Therefore, for a charge Q moving at a velocity v at an angle θ to magnetic field of magnetic flux density B:

F = BQvsinθ


Charged particles in circular orbits


Charged particle in a magnetic field


The cyclotron


The mass spectrometer


Charges in magnetic fields: summary


Generating electricity

Whenever a wire ‘cuts’ the lines of a magnetic field, an electromotive force (EMF) is induced in the wire. This effect is called electromagnetic induction.

move the wire faster

use a stronger magnet

use a coil of wire, and increase the number of turns.

It does not matter whether it is the wire or the field that is moving.

To increase the EMF:


Fleming’s right-hand rule

Fleming’s right-hand rule can be used to predict the direction of the induced current if the direction of force (motion) or the magnetic field are known.

thuMb = Motionof conductor

First finger = magnetic Field

seCond finger = Current

Fleming’s right-hand rule is sometimes known as the dynamo rule.


Explaining electromagnetic induction


Currents in a coil: the clock rule

In a long coil of wire or solenoid, the magnetic field line pattern is shown below.

At the south pole, current flows clockwise

At the north pole, current flows anticlockwise

Looking face-on at each end of the coil:


Lenz’s law


What is magnetic flux?

Magnetic flux () is the product of magnetic flux density and the area perpendicular to field. The area is the amount of field that has been ‘cut’ or ‘swept out’.

The unit of magnetic flux density is the weber (Wb).One weber is equal to 1 T m2.

= BA

magnetic flux = magnetic flux density × area

area, A

flux density, B


Magnetic flux linkage

Magnetic flux linkage (N) is a measure of the magnetic flux of a coil of wire.

N = BANcosθ

If the field is perpendicular to the coil, N is the product of the magnetic flux and the number of coils: N = BAN.

If the field is at angle of θ to the normal of the coil:

magnetic fluxlinkage

areamagnetic flux

density no.

coilscosθ×= × ×

normalθ

coil: N turns; A area

field lines


Faraday’s law of EM induction

Michael Faraday was the first person to show that an induced e.m.f. could be calculated from magnetic flux changes.

Faraday’s law of electromagnetic induction states that:

The induced e.m.f. in a circuit is equal to the rate of change of magnetic flux linkage through the circuit.

The negative sign indicates that the induced e.m.f. acts in such a direction as to oppose the change that causes it.

induced e.m.f., (or E) =-N

t


AC generator


Rotating coils in magnetic fields

In a simple AC generator, a coil rotates within a uniform magnetic field. The flux linkage changes continuously, because the angle of the coil (θ) changes continuously.

For a coil rotating at frequency f: θ = 2πftwhere t = 0 when θ = 0.

And therefore N = BANcos2πft. Plotting a graph of this:


E.m.f. induced in an AC generator

The gradient of the graph of the flux linkage of a rotating coil represents the change in flux linkage per second: NΔ / Δt.

The induced e.m.f. this produces can be calculated mathematically:

ε = BANωsinωtwhere ω is the angular velocity of the coil: ω = 2πf, and t is time.

the angular velocity (ω) (i.e. frequency of rotation, f)

The maximum, or peak, induced e.m.f., o, can be varied by altering:

the area or number of turns of the coil (A or N)

the strength of the magnet (B).


Induced e.m.f.: worked example

A coil with rectangular cross section (width 2 cm, length 3 cm) has 20 turns. It is rotated at a frequency of 20 Hz in a magnetic field of flux density 120 mT. What is the maximum induced e.m.f.?

Write down equation: ε = BANωsinωt

Maximum possible value for sinωt = 1, therefore εo = BANω

εo = 0.120 × (0.02 × 0.03) × 20 × (2 × × 20)

εo = 0.181 V

Substitute ω = 2πf: εo = BAN(2f)

Convert units: 120 mT = 0.120 T; 2 cm = 0.02 m; 3 cm = 0.03 m


Rotating coil in a magnetic field


Simple AC generator: summary


Transformers

primary coil secondary coil

A transformer changes the peak value of an alternating voltage.

Transformers consist of two coils: the primary coil and a secondary coil.

When an alternating voltage passes through the primary coil, an alternating magnetic field is created, which induces an alternating e.m.f. in the secondary coil.


The transformer rule

Ns

Ns

=Vs

Vp

Ns

Np

Np

Np

-Npt

Vp =-Ns

tVs =

Dividing the equation for the e.m.f. of the secondary coil by the one for the primary coil gives the transformer rule:

no. coils

primary coil secondary coil

flux linkage

induced e.m.f.

In a step-up transformer: Ns > Np so Vs > Vp.

In a step-down transformer: Ns < Np so Vs < Vp.


Transformer efficiency

The efficiency is very high for a typical transformer. A laminated core reduces eddy currents, the wires have very low resistance and a soft iron core allows easy magnetizing/demagnetizing.

transformer efficiency = power supplied by secondary coil

power supplied to primary coil

In a step-up transformer, voltage is stepped up and current is stepped down.

In a step-down transformer, voltage is stepped down and current is stepped up.

VsIs

VpIp

transformer efficiency =


Glossary


What’s the keyword?


Magnetic fields: equations summary


Multiple-choice quiz

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