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Electromagnetic Induction

Electromagnetic Induction

Faraday was working with two coils mounted on a

wooden spool. Whenever he put a large amount of

current into the primary coil, a small amount of

current was produced in the secondary coil. This

flow of current in the secondary coil was only

present for a very short time.

Michael Faraday

Using a galvanometer he was also able to detect a

small amount of current when the current to the

primary was turned off.

After a lot of further investigations he

determined that a changing magnetic field induced

(created) a current flow in another completely

separate solenoid.

Electromagnetic Induction

Demo Pass a Magnet quickly through a coil of

wire attached to a galvanometer.

The galvanometer will show a current flow when

the magnet moves in and out of the coil.

The strength of the magnetic field.

The amount of current that is induce depends on

The rate of change of the magnetic field.

The number of coils in the solenoid.

Electromagnetic Induction

This is known as Faraday's Law.

It describes the amount of emf (voltage) induced

when a coil of wire is subjected to a changing

magnetic field.

? emf (voltage) V

N number of coils in the solenoid

?F change in magnetic flux (Webber's Wb

?t change in time (s)?

Electromagnetic Induction

What is magnetic flux?

?F

It is a combination of the magnetic field

intensity and the area in which the magnetic

field lines are in.

?F ?BA

The combination of BA must be changed in order to

generate an induced current.

B magnetic field intensity (Tesla)?

A Area of the coil or magnetic field (m2)?

Electromagnetic Induction

a)?

Examine each of these two side-by-side magnetic

flux situations. Do you see why the left side has

the greatest magnetic flux?

b)?

The Magnetic flux is increasing as the ring is

moving upwards. Why?

c)?

Electromagnetic Induction

Example 1

A 200 turn circular coil of radius 0.15 m is

quickly rotated in a time of 0.12 s from being

perpendicular to being parallel to a 0.56 T

magnetic field as shown below.

?t 0.12 s

What is the average induced emf (voltage)?

Electromagnetic Induction

Solution

66 V

?

(The negative sign is just there to remind us in

which direction the induced current is going.)?

Electromagnetic Induction

Example 2

A coil having 45 loops and as area of 0.35 m2 is

initially placed perpendicular to 0.75 T magnetic

field. The field is reversed in direction to a

magnitude of 0.62 T in a time of 0.25 s. The coil

is connected to a 40 ohm resistor. What is the

magnitude of the current through the resistor?

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Electromagnetic Induction

Solution

86.31 V

Electromagnetic Induction

Remember Ohm's Law!

But what about the direction of the current?

This will take a little explaining!

Electromagnetic Induction

Lenz's Law

The induced emf always gives rise to a current

whose own magnetic field opposes the original

change in flux.

The coil is squished together reducing the area

to zero. Which direction will the induced current

flow in the coil during the collapse?

Electromagnetic Induction

What is the direction of the induced current in

the coil as the magnetic field is reversed?

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Electromagnetic Induction

Another Example

A bar magnet is quickly brought near a single

coil of copper wire.

v

What direction will the current flow in the

copper coil when the magnet is brought closer to

the coil?

Electromagnetic Induction

One last example

What direction will the current flow through the

meter as the bar magnet is pulled out?

Answer Current will Downwards through the meter

Electromagnetic Induction

EMF Induced in a Moving Conductor

?A

L

v x ?t

N?BA

?

But A L x(v x ?t) N 1

?t

Electromagnetic Induction

B x L x(v x ?t)?

?

?t

This equation will determine the voltage placed

across a conductor as it moves in a magnetic

field.

Example

x x x x x x x x

x x x x x x x x

v 5.6 m/s

?

1.9 V

L 0.45 m

x x x x x x x x

(The top of the conductor will become positively

charged! right hand rule)?

x x x x x x x x

x x x x x x x x

B 0.75 T

Electromagnetic Induction

The back (or Counter) Emf in a Motor

A motor simply a set of coils with current

running through them placed in a magnetic field.

The split-ring commutator allows the current to

change direction every ½ turn keeping the motor

coil turning.

Motor Demo

But the turning coil crossing the field lines

generate a induced current that opposes the

original applied current that makes the motor

turn.

Electromagnetic Induction

This induced current produces an opposing voltage

called back emf. It acts against the voltage

causing the motor to spin in the first place.

As the motor spins up to speed the back emf

increases in value until most of the applied

voltage is cancelled out.

At start up the motor only sees the applied

voltage. Since the resistance of the motor is

relatively constant the motor draws a lot of

current when starting up.

Most heavy duty motors found in refrigerators or

table saws have a start capacitor which supplies

some of this current at start up so that it

doesn't trip the circuit breaker when the motor

is first turned on. (In older homes you may have

noticed that some lights in a kitchen dim when

the refrigerator motor (compressor) turns on.)?

When the motor is running at full speed there is

lots of back emf. The effective voltage across

the motor is much less than at start up.

Electromagnetic Induction

Since the effective voltage is reduced when the

motor is running at full speed, so then is the

current required. A motor running at full speed

requires much less current than at start up.

(Once the refrigerator motor is running at full

speed the lights go back to their usual

brightness).

A very similar effect can cause an electric drill

to burn out its motor. If the drill is being

used to drill a hole and the drill bit is grabbed

and held stationary, the back emf through the

drill's motor is reduced to zero. The current

through the motor goes very high. High enough in

some cases to melt the wires in the motor

windings and burn outthe drill's motor.

Electromagnetic Induction

Vb Emf - IR

Vb back emf

Emf voltage applied to the motor

I current applied to the motor

R resistance of the motor (constant)?

Electromagnetic Induction

Example

The armature windings of a motor have a

resistance of 8.0 ohms. The motor is connected to

120 V. The motor draws 2.0 A while running at

full speed.

a) What current is drawn by the motor at start up?

120 V

15 A

8.0 O

b) What is the back Emf when the motor is running

at full speed?

Vb 120 V - 2.0 x 8.0

104 V

Electromagnetic Induction

Transformers

Electromagnetic Induction

A transformer is used to either increase

(Step-UP) or decrease (Step-Down) the voltage for

various uses.

Transformers consist of two separate coils of

wire and usually a conducting iron metal support.

It is the arrangement of the two coils that

creates either a step-up or step-down transformer.

Transformers only work with AC (alternating

Current)!

Electromagnetic Induction

The transformer is very efficient device. It has

no moving parts. The two coils that make up the

transformer are not in contact with each other so

how is it able to change the voltage?

The answer lies in using AC (alternating current)

to create a changing current flow which produces

a changing magnetic field on one side of the

transformer. This induces a changing magnetic

field on the other coil which induces a new

current flow in this coil.

Since the only a changing magnetic field will

induce a new current, the transformer only works

if the current is AC (which is changed 60 times

every second).

Let us examine how to work with the transformer

equations.

Electromagnetic Induction

For all ideal Transformers

Energy In Energy Out

And Energy Power x Time

Power x time In Power x time Out

Power In Power Out

And Power V x I

Electromagnetic Induction

Transformer Equation

Vinput x Iinput Voutput x Ioutput

Vi x Ii Vo x Io

Electromagnetic Induction

Let us have another look at Faraday's law and

apply it to transformers

N?BA

?

Remember ? voltage

?t

Vi x Ii Vo x Io

Replace the V on each side with Faraday's Law

No?BA x Io

Ni?BA x Ii

?t

?t

The B and A and t are the same on both sides and

cancel each other out.

Electromagnetic Induction

This results in a new equation

NiIi NoIo

Putting this equation with the Power one results

in

Vi

Ni

Io

Vo

No

Ii

Electromagnetic Induction

Example

A small step-down transformer is plugged into a

wall outlet supplying 120 V. The transformer has

1800 windings on the input side and 40 windings

on the output side. The input current is 0.0050 A.

a) What is the output voltage of this

transformer?

Vi

Ni

Vo

No

Vo (Vi x No)/Ni

2.7 V

Vo (120 x 40) / 1800

Electromagnetic Induction

b) What is the output current of this

transformer?

Vi

Ni

Io

Vo

No

Ii

Io (Vi x Ii) / Vo

Io (120 V x 0.0050 A) / 2.7 V

Io 0.22 A

c) What is the power of this transformer?

P V x I

2.7 V x 0.22 A

0.59 W

Electromagnetic Induction

Large Transformers used in Power and Sub-stations.

These transformers convert high voltage to lower

household voltage.

Small Transformers used in converting 120 V to

6.0 v for small devices.

Electromagnetic Induction

Transformers are used for stepping up voltage to

very high values for efficient transmission over

long distances from power stations and also used

to reduce voltage to more household friendly

voltage of 240 V.

Electromagnetic Induction

But why is electrical energy transported at such

high voltage? Why do we have high voltage power

lines that cross our province?

First of all large scale power production is

usually done far away from populated centers.

Dams are usually created across large rivers at

some distance from a large urban center. Like

wise for large thermal generating plants or

Nuclear power plants.

Second of all no electrical transportation system

is 100 efficient. All electrical wires have some

resistance and hence generate heat when current

is flowing in the wires.

Third the amount of energy lost per second in a

power line called Power loss can be calculated

from this equation

I current in the wires

PL I2R

R resistance of the wires

Electromagnetic Induction

Typically the resistance in power line wires is

quite small at around 5 10 ohms.

The current flow on the other hand can be quite

significant as power (energy) has to be supplied

to all those who need it.

Lets us do a sample calculation as to why high

voltage is used to transport electrical energy

Typically power stations generate power at 5 -

15000 MW (5 million watts to 15 billion watts) at

around 500 V and around 10000 or more Amps

Assuming a resistance of 10 O in the wires what

would be the power loss if the electrical energy

was transported at this voltage and current.

Electromagnetic Induction

Assuming Current is 10000 A and resistance is 10

O then the power loss would be

PL I2R

PL 100002 x 10

PL 1000000000 W

PL 1000 MW

This is 200 x the available energy!!!!

The wires would get very hot and maybe melt. This

would be one huge toaster and no power would

reach those who needed it!

Electromagnetic Induction

Now let us redo the calculation but use a

transformer to increase the voltage up to high

values.

Remember

P VI

Since the same power has to be delivered by

increasing the voltage the current has to be

decrease!

Let's increase Voltage to 250000 V

5 x 106 W 250000 x I

I 5 x 106 / 250000

At a high voltage of 250 KV only 20 amps of

current is needed

I 20 A

Electromagnetic Induction

Re-doing the Power Loss calculation at the new

current

PL I2R

PL 202 x 10

PL 4000 W (A good size electric Heater)

This an insignificant amount of power loss and

would allow a delivery of 99.92 of the energy

produced!

Remember transformers themselves are very

efficient as well so very little power is lost in

using them.

The high voltage that power is transmitted at is

too dangerous to use the consumer level so

step-down transformers change it back to a more

manageable level.

Electromagnetic Induction

Have another look at the transmission diagram.

You should now have a good understanding of why

all the changes in voltage have to happen.

Electromagnetic Induction

This the end of electromagnetism and of Physics

12!

I hope you found it both interesting and

challenging.

Good luck on your final exams and next year!

Electromagnetic Induction

Electromagnetic Induction

Electromagnetic Induction

Electromagnetic Induction

Electromagnetic Induction

Electromagnetic Induction