emi lecture 26 mar 2010 (student version)

8/9/2019 EMI Lecture 26 Mar 2010 (Student Version)

1/45

For NJC internal use only; No parts of these slides shall be reproduced without prior permission from NJC.

EMI Lecture

26 Mar 2010


2/45


Worked Example 6.1

The original field is INTO the plane.

This flux is now decreasing.

EMF is induced and current flows.

Induced current flows to maintain

this flux.

Induced current flows in theclockwise direction to set up a Bfield that points INTO the page.


3/45


Worked Example 6.1

Original field is pointing OUT of

the page.

Now the flux is decreasing.

To maintain the flux, instead ofcausing further decrease, theinduced current flows in anti-clockwise direction to set up a Bfield pointing OUT of the page.


4/45For NJC internal use only; No parts of these slides shall be reproduced without prior permission from NJC.

Lets go back to Page 13



Lenzs Law is a consequence of the law

of conservation of energyP

Q

By simply moving the rodPQ in a magnetic field, we

create a current,I, flowingthrough the resistor R.

In a way, the rod PQ acts

as a source of emf,providing current =I= /R.

Electrical power, P,delivered to R =I2R = 2/R= B2l2v2/R



No free lunch in this world

Emf represents theamount of energy

converted from otherforms to electrical. For instance, chemcial ->

electrical in battery

For instance, solar ->electrical in solar panel

So the electrical powerfrom the induced emfdissipated in R must havebeen converted fromother forms.



No free lunch in this world The electrical power from

the induced emfdissipated in R must havebeen converted from thework done by Fapp, thepulling force.

The rod is pulled at

constant velocity i.e. KEof rod is constant.

This means there is a

force opposing Fapp suchthat Fnet = 0 Induced current flows in therod surrounded by magneticfield. This results in a

magnetic force FB2 actingon rod.

FB2

This is Lenzs Law at work!The induced current has toflow in a direction to opposethe change that causes it.


8/45


No free lunch in this world

Fapp = FB2.

Hence Fapp = BIL (or is it BLv?) What is the rate of work done by

Fapp? Fapp v

BILv = BLv (/R) =

B2L2v2/ R

What happens to this power?

FB2

Mechanical

work done by

Fapp

Electrical

Energy

dissipated

in R


9/45


Lenzs Law

Used to predict andexplain polarity of

induced emf or direction

of induced current;

Arises from conservationof Total Energy


10/45


Faradays law

To produce aninduced e.m.f.

Rate of change ofmagnetic fluxlinkage

Rate of flux-cutting

Magnitude ofthe emf is

proportional to

Magnitude ofthe emf is

proportional to


11/45


Page 16

Emf is induced in a circular loop conductor

when flux through it changes. Emf is induced across a straight conductor

when it cuts across a magnetic field. Now what if a loop conductor moves in a

magnetic field?


12/45


What happens when a loop conductor cuts themagnetic field?

VL inducedcurrent


13/45



V

Net induced e.m.f.= zero


14/45



V

inducedcurrent

Wh h h l d h


15/45



VLinducedcurrent

Looking at the magnetic flux instead

Area of the coil withinthe magnetic flux density

This area (i.e.magnetic flux) is

increasing as the coilmoves into the field.

Hence, rate of

change of magneticflux induced e.m.f.

Wh t h h l d t t th


16/45



VLinducedcurrent

Considering fluxcutting by QR

= BLv

P Q

RS

Wh t h h l d t t th


17/45



V


The magnetic flux of coilremains unchanged.Hence, by Faradays

law, no induced e.m.f.

P Q

RS

Wh t h h l d t t th


18/45



V

If consider flux cutting

Sides PQ and RS

do not cut the Bfield and hence noemf is induced

across PQ or RS.

P Q

RS

Sides PS and QRcut the B field and

hence emf isinduced across PSor QR.

What happens when a loop conductor cuts the


19/45



V

inducedcurrent


The magnetic flux of coilis now decreasing. Hence,

by Faradays law, there is

induced e.m.f.

What happens when a loop conductor cuts the


20/45



V

inducedcurrent

This induced e.m.f. = Blv


21/45


Example 7.1

180 ms-150 m

The wingspan cuts the Earths fieldand induces an emf across it.

V


22/45


What happens if the loop conductorrotates within the B Field?

Ch i th l


23/45


Changing the angle

Ch i th l


24/45


Changing the angle

When increases from 0 to 90

Ch i th l


25/45


Changing the angle


Changing the angle


26/45


Changing the angle


Changing the angle


27/45


Changing the angle


Themagnetic fluxdecreases

Changing the angle


28/45


Changing the angle

How does the induced current flow?


Changing the angle


29/45


Changing the angle



30/45


Changing the angle If the coil rotates constantly (i.e. with

angular frequency ), the magnetic flux

linkage is given by

= NBA cos

= NBA cos (

t)Induced e.m.f. = - (rate of flux change)

=

tNBA

tdt

dNBA

sin

)(cos

=


31/45


Example 7.3

= NBA cos (t) or

NBA sin (t)

depending if ismax or min at t = 0

At t = 0


32/45


= NBA cos (t) or NBA sin (t)

= NBA sin(t) or -NBA cos (t) What is important to note is that the

induced emf is sinusoidal! This is the AC voltage you have studied

last year end.


33/45


Example 7.2

(b) Spinning the coil faster increases and so does

(c) Increasing the magneticfield

B increases and so does

(a) Replacing the coil wirewith one of lowerresistance

No change to ;

R is smaller and henceinduced ,I, increases.

(d) Increasing the number ofturns of wire on the coil

N increases and so does ;

I may not increase. Do you

know why?

How to increase the induced emf, = NBA sin(t) ?


34/45


Eddy Current

When a conductor is exposed to a changingmagnetic field, circulating current flows withinthe body of the conductor.

This current is called eddy current.

Eddy current flows in a direction that opposesthe change of flux due to Lenz's law, causingdrag forces between the conductor and the

magnet.

Larger the current, the larger the drag force.
http://en.wikipedia.org/wiki/Conductor_(material)http://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Lenz%27s_lawhttp://en.wikipedia.org/wiki/Lenz%27s_lawhttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Magnetic_fieldhttp://en.wikipedia.org/wiki/Conductor_(material)


35/45


Demo 1

The flux through the copper ring increases

and decreases as the falling magnetapproaches and recedes from the ring.

Emf is induced.

Induced (eddy) current flows in the ring soas to oppose the change.

What exactly happens to the magnet asthe current flows to oppose the change?


36/45


Applications of Eddy Current

Magnetic Braking

S

N


37/45



Magnetic Braking see Example 8.1

S

N


38/45

A li i f Edd C


39/45



Magnetic Braking see Example 8.1

S

N

How to slow down the plateeven more?

Strengthen the field;

Use a plate with lowerresistance;

E l 8 1


40/45


Massbalance

Metal plate moving upand down between

magnetic poles

Example 8.1

A li ti


41/45


Applications

Metal Detector

See Animation of how VLF metal detectorswork:

http://home.howstuffworks.com/metal-

detector2.htm

Induction Stovetops

A li ti
http://home.howstuffworks.com/metal-detector2.htmhttp://home.howstuffworks.com/metal-detector2.htmhttp://home.howstuffworks.com/metal-detector2.htmhttp://home.howstuffworks.com/metal-detector2.htm


42/45


Applications

A li ti


43/45


Application

Speakers and microphones


44/45


inducedcu

rrent


45/45


The End

emi lecture 26 mar 2010 (student version)

Documents