remember? an electron is moving downward with a velocity, v, in a magnetic field directed within...

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

Moving conductor



Yes magnetic force… which direction is it acting?

+++

– – –

R

Moving conductor



Yes magnetic force… which direction is it acting? – upward

So when you’re pushing it downward, what energy is it gaining?

+++

– – –

R

Force applied

Magnetic force

Moving conductor Which direction were we

pushing this conductor?


Yes magnetic force… which 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 unit: Tm2, Wb


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?

resisto

r

Question

What will happen if you remove the magnetic field suddenly?

resisto

r

Question

BRING BACK THE FIIIEEEELLLDDD!!! LENZ’S LAW

resisto

r

Question

to get the field back, which direction should the induced current be?

resisto

r

Question

Current upward…. Force????

resisto

r

Question

Current upward…. Force to the right… and off it goes…..

resisto

r

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

remember? an electron is moving downward with a velocity, v, in a magnetic field directed within...

Documents

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magnetic force slide

r r force

moving conductor e force

direction of force

moving conductor epe

moving conductor conductors

metal conductor