Electromagnetic induction

Electromagnetic induction

Topic 12

Remember? An electron is moving downward with a

velocity, v, in a magnetic field directed within the page, determine direction of force.

Moving conductor Conductors contain free

electrons So when a conductor moves

downward, electron will experience a magnetic force pulling them to the left.

Lattice atoms on the right become positive…

There is a potential difference now

Moving conductor E force produced wanting to

push electrons to the right Forces are now balanced and

electrons will stop moving What will happen if you connect

a resistor to the metal conductor?

Moving conductor E force produced wanting to

push electrons to the right Forces are now balanced and

electrons will stop moving What will happen if you connect

a resistor to the metal conductor?

Current will flow from high to low potential

+++

– – –

R

Moving conductor What did we define emf

previously as? Amount of chemical energy

converted to electrical energy per unit charge

+++

– – –

R

Moving conductor What did we define emf

previously as? Amount of chemical energy

converted to electrical energy per unit charge

We don’t have chemical energy here!!!

Where does our energy come from here?

+++

– – –

R

Moving conductor Which direction were we

pushing this conductor? Another force acting on

conductor?

+++

– – –

R



conductor? Yes magnetic force… which

direction is it acting?

+++

– – –

R




direction is it acting? – upward So when you’re pushing it

downward, what energy is it gaining?

+++

– – –

R

Force applied

Magnetic force




direction is it acting? – upward So when you’re pushing it

downward, what energy is it gaining? – EPE

You are doing work If forces are equal, conductor is

moving at constant v.

+++

– – –

R

Force applied

Magnetic force

Moving conductor EPE will be converted into heat Energy is conserved

Now let’s define INDUCED EMF? Amount of mechanical energy

converted into electrical energy per unit charge.

+++

– – –

R

Force applied

Magnetic force

Calculating induced EMF

Maximum p.d. in conductor is when the magnetic force ON ELECTRON is equal to the electrical force

–L

Calculating induced EMF

Maximum p.d. in conductor is when the magnetic force ON ELECTRON is equal to the electrical force

Electron will stop moving.. Therefore greatest p.d.

Equate equations

–L

Induced EMF equation

*

*

The induced EMF will be the same as p.d. across conductor

Question If magnetic field not perpendicular to

direction of motion… what will you do?

v

B

Question If magnetic field not perpendicular to

direction of motion… what will you do?

Take the B that is perpendicular to v

QUESTION

THREE HAND RULESRIGHT LEFT

Faraday’s law What generated induced emf? What did it depend on?

Faraday’s law What generated induced emf? – moving

conductor in a magnetic field What did it depend on? Faraday’s law:

The induced emf is equal to the rate of change of flux

Flux VS flux density Let’s look at this analogy

Flux VS flux density How much grass do you have? Is it taking lots of area?

Flux VS flux density Pieces of grass is flux density (B) Area over which grass takes over is flux (Φ)

Flux VS flux densityFlux unit: Tm2, Wb

Flux VS flux density

Normal to surface

If area at angle from B Find component of B that will be

perpendicular to area

θ

Lenz’s law Moving conductor in magnetic field causes

a force to oppose the direction of motion as seen earlier (if not true than energy will not be conserved)

Lenz’s law is an extension to Faraday by stating that: the induced current will be in such a direction

as to OPPOSE THE CHANGE IN FLUX that created the current.

Question

Question Determine direction of current

Question

Question Rail gun… how does it work?

resistor

Question What will happen if you remove the

magnetic field suddenly?

resistor

Question BRING BACK THE FIIIEEEELLLDDD!!! LENZ’S

LAW

resistor

Question to get the field back, which direction should

the induced current be?

resistor

Question Current upward…. Force????

resistor

Question Current upward…. Force to the right… and

off it goes…..

resistor

Question

Question http://science.howstuffworks.com/rail-gun1.htm

Read Applications of EM induction on page 213

Alternating current (AC)

What’s the difference between a motor and a generator?


What’s the difference between a motor and a generator?

Motor electrical to mechanical energy Generator mechanical to electrical


What’s the direction of current induced here?


What’s the flux going to be at angle 0?


What’s the flux going to be at angle 0? Maximum since

So how will the graph look like?


Label the positions in graph

Alternating current Since we have many loops here we change

the equation a bit and add “N” so that the total flux (called flux linkage):

Can we substitute θ with something else?

Alternating current .


How will the emf graph with time look like? What’s the emf equation?



How can we get this value from the flux vs time graph?



How can we get this value from the flux vs time graph? ---- (negative the gradient)


So will the equation for emf have a sin or cos?


So will the equation for emf have a sin or cos?

Therefore at 90 degrees the emf in max and the flux is zero.

Emf and time Emf vs time graph… what will happen if you

double the angular speed…

Emf and time Emf vs time graph… what will happen if you

double the angular speed… Double emf and half the period

Current and time How can the current in the circuit be found?

Current and time How can the current in the circuit be found?

ε0 is equal to:

Can you think from where this equation came from?

Graphs

Definitions AC: current delivered by rotating coil

changing in direction and size over period of time

DC: constant current delivered from battery

question

Answer

Power Equation(s)?

Power P=IV, let substitute…

always positive

Power Average power is about 50W in example

below… how about the average current and voltage from previous graphs?

Power Average power is about 50W in example

below… how about the average current and voltage from previous graphs?

ZERO???? How do we solve this?

RMS To solve this by calculating the root mean

square (rms) Square voltage or current then divide by

two then square root the answer

Question

Power loss Power transmitted through wire will be lost

due to what factors?

Power loss Power transmitted through wire will be lost due to

what factors? P=I2R [power loss to heating] To reduce heat loss we have to reduce I Reducing current, if DC was transmitted through

power lines that feed homes, will have nothing left to run instruments..

AC, on the other hand, keeps on changing current and voltage…

Power loss P=IV

So if we increased V then I will decrease since power supply in constant

So if we increase voltage by 100V, then the current will be less (I /100)

So the power loss will be reduced by 1002 (P=I2R) WOW very useful and can only happen in AC Ok… how can we do this? Transformers

Transformers NO! Not the movie :p

Transformer

Current runs through primary.. What will it generate?

iron

Transformer

Current runs through primary.. What will it generate? A magnetic field will be generated in all iron

(that’s why it has to be a magnetic metal) Now there is a magnetic field in in

secondary coil.. What will happen?

iron

Transformer

Current runs through primary.. What will it generate? A magnetic field will be generated in all iron (that’s

why it has to be a magnetic metal) Now there is a magnetic field in in secondary coil..

What will happen? NOTHING How can we make a current run through the

secondary coil?

iron

Transformer

Current runs through primary.. What will it generate? A magnetic field will be generated in all iron (that’s

why it has to be a magnetic metal) Now there is a magnetic field in in secondary coil..

What will happen? NOTHING How can we make a current run through the

secondary coil? CHANGE THE FLUX – INDUCED EMF

iron

Transformer

CHANGE IN FLUX created a current Potential difference in primary coil is

proportional to number of loops

so

iron

Transformer

So lets look at the example above Number of loops in secondary is greater

than primary So voltage in secondary will also be larger

than primary So how about the current?

iron

Transformer

Look at above equation Since voltage is more than the current will

be less (since the power is constant). So we just have MORE VOLTAGE (10/5 so

double voltage) :D Step up transformer

iron

Transformer

Step up transformer to transport from plant to houses

Step down transformer at home to devices

iron

Transformer

Question

answer

Read For more information 218 and 219

Electromagnetic induction

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