Magnetism and Magnetism and InductionInduction

NCEA AS 3.6NCEA AS 3.6

Text Chapters: 15,16,17Text Chapters: 15,16,17

ElectromagnetismElectromagnetism

Fields are formed around current Fields are formed around current carrying wires carrying wires

SolenoidsSolenoids

Fields are Fields are formed in formed in solenoids or solenoids or coils.coils.

InductionInduction

If a wire is moved If a wire is moved through a magnetic through a magnetic field then a voltage field then a voltage can be can be inducedinduced across the ends the across the ends the wire.wire.

InductionInduction

If the wire is If the wire is connected to a circuit connected to a circuit then current will flow. then current will flow. The direction of The direction of induced current is induced current is determined by a right determined by a right hand rule.hand rule.

Right Hand Slap RuleRight Hand Slap Rule

v=direction of wire v=direction of wire movementmovement

B=direction of B=direction of magnetic field linesmagnetic field lines

F= force on a positive F= force on a positive charge (ie direction of charge (ie direction of current flow)current flow)

InductionInductionThe size of this induced voltage is given by:The size of this induced voltage is given by: V=BvLV=BvL (B=mag field strength, (B=mag field strength, v=velocity of movement, v=velocity of movement, L=length of wire in field)L=length of wire in field)

This is known as This is known as Faraday’s LawFaraday’s Law

InductionInductionThe direction of the induced current is The direction of the induced current is such that it creates an opposing force on such that it creates an opposing force on the motion that is causing it.the motion that is causing it. This is known as Lenz’s LawThis is known as Lenz’s Law

Opposing Force F=BIL

Direction of movement

Induced current I

InductionInduction

Induced voltage/current can be made Induced voltage/current can be made larger if:larger if: The mag field is strongerThe mag field is stronger The wire is longerThe wire is longer The movement is fasterThe movement is faster (Solenoid has an iron core)(Solenoid has an iron core)

InductionInductionInduction can also occur if it is the magnetic Induction can also occur if it is the magnetic field that is moved, rather than the wire.field that is moved, rather than the wire.

Magnetic FluxMagnetic Flux

The magnetic field in a The magnetic field in a circuit is measured as circuit is measured as magnetic flux magnetic flux ΦΦ

ΦΦ= BxA= BxA B = mag field strengthB = mag field strength A = area perpendicular to A = area perpendicular to

field field

The unit for flux is the The unit for flux is the Weber WbWeber Wb

Magnetic FluxMagnetic Flux

A useful analogy is A useful analogy is using a net to catch using a net to catch whitebait in a whitebait in a stream….stream….

If you don’t hold the If you don’t hold the net straight up and net straight up and down, you don’t catch down, you don’t catch many whitebait!!many whitebait!!

Faraday’s LawFaraday’s Law

According to Faraday’s Law, V=BvLAccording to Faraday’s Law, V=BvL

The area of the loop in the field is zero…..The area of the loop in the field is zero…..

LSpeed v

Faraday’s LawFaraday’s Law

Some time t later, Some time t later, A has changed by A has changed by ΔΔA = A = (vt x L)(vt x L)

ΔΦΔΦ = B x = B x ΔΔAA

ΔΦΔΦ = B x v x L x t = B x v x L x t

But V=BvLBut V=BvL

So So ΔΦΔΦ = V x t = V x t

L A v

Faraday’s Law (again)Faraday’s Law (again)

Another way to look at Faraday’s Law is that Another way to look at Faraday’s Law is that the induced voltage in a circuit is determined the induced voltage in a circuit is determined by the by the rate of change of fluxrate of change of flux

tV

The negative sign is a

reminder of Lenz’s Law

GeneratorsGeneratorsRather than sliding a loop through a field, it is Rather than sliding a loop through a field, it is easier to spin it.easier to spin it.

This is how a generator worksThis is how a generator works

GeneratorsGenerators

When the coil is When the coil is horizontal, the horizontal, the induced current is induced current is maximum, as the maximum, as the coil is cutting coil is cutting across the field across the field lines at right lines at right angles as it angles as it moves.moves.

GeneratorsGenerators

When the coil is When the coil is vertical, the vertical, the induced current induced current is zero, as the is zero, as the coil is moving coil is moving parallel to the parallel to the magnetic field magnetic field lines lines

GeneratorsGenerators

If we start timing from when the coil is vertical, If we start timing from when the coil is vertical, then at t=0, then at t=0, ΦΦ= BxA= BxA

N S

B

A

GeneratorsGenerators

If the coil rotates with speed If the coil rotates with speed ωω, then after , then after time t the coil will have turned through time t the coil will have turned through angle angle θθ = = ωωtt

The flux will now be The flux will now be ΦΦ= Bcos= Bcosωωt x At x A

N S

A

Bθθ

GeneratorsGenerators

Faraday’s Law says: Faraday’s Law says:

For a coil of N turns:For a coil of N turns:

tBAVdt

tBAdV

dt

dV

sin

)cos(

tBANV sin

GeneratorsGenerators

The formula for alternating generator voltage is The formula for alternating generator voltage is often written as:often written as:

Where VWhere Vmaxmax=BAN=BANωω

This produces a voltage-time graph that looks This produces a voltage-time graph that looks like a sine curvelike a sine curve

NB. Similarities to SHM!!NB. Similarities to SHM!!

tVV sinmax

GeneratorsGenerators

To generate A.C, To generate A.C, slip ringsslip rings are used… are used…

GeneratorsGenerators

To generate D.C, To generate D.C, split ringssplit rings are used. are used.