Electromagnetic Induction

Electric Fields• Electric fields are created bycharges

• A charge in an electric field always has a force on it

+force

Magnetic FieldMagnetic fields are created by moving charges

This can happen inmagnets or current carrying wires.

Magnetic Fields only affect moving charges

+ +

velocity

FORCE is… ZERO FORCE is…

towards you

strong field

weak field

strong field

weak field

NS

electron beam

electron gun

x

y

z

What direction is the magnetic field?

NS

wire

Wire's velocity

x

y

z

Magnetic Flux

• Magnetic flux is the amount of magnetic field.

• It depends on the field strength and the area

NS

There is a large flux through this loop

And a smaller flux through this loop

Even smaller flux through this loop

Which ring has the biggest magnetic flux in it?

Which ring has the strongest magnetic field strength in it?

Magnetic field lines

Which ring has the largest magnetic flux in it?

Magnetic = Magnetic X Area

Flux Field Strength

Webers = Tesla x m2

B A

• Magnetic field strength is also called flux density.

BA

B A

Which ring has the biggest magnetic flux ?

Area is same

Field strength is same

Which ring has the biggest magnetic flux ?

• Year 12:A wire cutting across a magnetic field has an

induced EMF (or voltage)

Faraday’s LawWhen the magnetic flux through a loop

changes, there is an induced EMF (voltage)

The faster the change, the bigger the EMF

t

Changing the Flux

• You can change the flux by changing the field strength or the area perpendicular

B A

NS

Changing the field strength

NS

Changing the area

NS

Changing the area perpendicular

Flux Change in a Generator

• faraday-mx.swf

• So for many loops,

t

becomes,

N

t

Changing the actual area Changing the angle

Changing the Area

Flux change in a moving loop

flux

time

voltage

time

Induced EMF in a moving loop

t

voltage

time

time

flux

Close switch… current increases …field increasesFlux change through 2nd coil

Induced EMF in 2nd coil

Creates current in 2nd coil

Creates magnetic field that opposes the cause.

N N

Lenz’s Law Electron flow

Force on roller

1: electrons in roller are moving 2: causing them to be pushed 3: electrons in roller are now flowing 4: causing them (and roller) to be pushed

• Faraday: A flux change causes an induced EMF (voltage)

• Lenz’s Law states that the induced voltage opposes the flux change that caused it.

t

NFalling magnet creates a flux change in the pipe.

This creates induced EMF

This creates induced current

This creates induced magnetic field

magnetic field opposes flux change

So how does your electric toothbrush charge up?

Increasing current in Primary

Causes flux change in core Causes flux change in Sec Causes induced EMF in Sec Causes induced current in Sec

This is called Mutual Induction

P

S

AC Generator

• http://www.walter-fendt.de/ph11e/generator_e.htm

B

A

C

D

VoltageAngle

FluxAngle

Coil position (End on)

VoltageAngle

FluxAngle

• ..\faraday.jar

Transformers

• A transformer is used to increase or decrease the voltage.

• Mains voltage in NZ is 240 V AC.

• Your cellphone charger needs about 4.0 V. It uses a transformer to reduce the voltage.

Increasing current in P

Causes flux change in P

Causes flux change in S

Causes induced EMF in S Causes induced current in S

This is called Mutual Induction

P S

• transformer.jar

Primary currentMagnetic flux in coreInduced EMF in Secondary

The AC current in the primary coil is changing sinusoidaly

So the magnetic flux is changing sinusoidally

So the induced EMF is sinusoidal

• The output voltage (Vs) depends on:

the input voltagethe ratio of turns

orp

ss

p

VN

NV

s

p p

sN

N V

V

VsVpprimary secondary

Iron core

Np Ns

Mutual Induction

• This is when a changing current in one coil induces a voltage (EMF) in a second coil.

Small Mutual Inductance between coils

Iron cores produce stronger, more concentrated magnetic field

larger Mutual Inductance

Toroidal core produces even larger

Mutual Inductance

M is the mutual inductance, measured in Henries (H)

EMF in secondary coil PMI

t

• Using transformers to save energy

You’ve seen these around the streets. What do they do?

Transformers are very important for power transmission.

• The power transmitted along wires is given by:

Power = V x I• The power wasted as heat in the

wire is given by :

Power = I2 x R

• To minimise the power lost as heat, the wire’s resistance and the current must be a small as possible.

Power lost = I2 x R

• To transmit the same power, the voltage must be very large.

Power transmitted = V x I

Power station generators produce electricity at about 4000 V

Transformers increase it to about 400 000 V. (and reduce the

current)

Transmission lines then carry the electricity at 400 000 V

Transformers in Auckland reduce the voltage to about 4000 V

This is then reduced to 240 V in local transformers around the

streets

4000 V400 000 V

4000 V

240 V

Your cellphone charger changes the 240 V current to about 4 V

• http://phet.colorado.edu/web-pages/simulations-base.html

Inductors

An inductor is a wire coil usually wrapped around an iron core

Self Inductance

A coil can induce a voltage in itself !!!??

A

Predict what happens when the switch closes.

What does happen when the switch closes?

A

What happens when the switch opens?

A

An inductor is designed to oppose a changing current

This is because it can induce an EMF in itself. This is called Self

Inductance.

Increasing current

Causes increasing magnetic fieldThere is a flux change through coilCauses induced EMF

Direction of EMF opposes current change

Increasing current

Induced EMF

Current Increasing

Self Inductance

• A coil can induce a voltage in itself.

• L is called the self inductance

EMF in coil PI

tL

Self Inductance (L) is measured in Henries (H)

• This induced EMF (or back EMF) opposes the increase in current, so the current rises…

SLOWLY

This is called Self Inductance

(The coil induces an EMF in itself)

current

timeClose switch

I = V/R

R is the ohmic resistance of the inductor L

R

current

Close switch

Back EMF

Close switch

Recall: EMF in coil PI

tL

timeClose switch

Imax

L

R

Recall the meaning of time constant for a capacitor and resistor?

It means the same for an inductor and resistor.

0.63 Imax

L

R

Larger inductance, longer time to reach maximum current

Larger resistance, smaller current so shorter time to reach maximum current

current

Close switch

How would the graph change if:

Inductor had higher inductance?

Inductor had higher resistance (careful)

Decreasing current

Causes decreasing magnetic fieldThis is a flux change

Causes induced EMF

Direction of EMF opposes current change.

Current Decreasing

• This induced EMF (or back EMF) opposes the decrease in current, so the current drops…

SLOWLY

This is called Self Inductance

When the switch opens, the current drops to zero rapidly

This causes a large flux change

This induces a very large EMF

This causes a spark across the switch

Mutual Inductancehttp://

phet.colorado.edu/web-pages/simulations-base.html

http://www.walter-fendt.de/ph11e/osccirc.htm

Extension: LC oscillation