CONCLUSION – CHAPTER CONCLUSION – CHAPTER 20 &20 &

CHAPTER 21 – CHAPTER 21 – ELECTROMAGNETIC ELECTROMAGNETIC INDUCTIONINDUCTION

Chapter 21

Quick Review IB

Magnetism2

r(exact) 104

2

70

0

A

Tm

r

IB

Magnetism3

Force Between Two Current Carrying Conductors

First wire produces a magnetic field at the second wire position.

The second wire therefore feels a force = Bil

Solenoid

Magnetism4

Length

Turns of

number Total0

L

Nn

nIB

B=~0 outside

The Toroid–

Magnetism5

r

NIB

20

B=0 outside

Magnetism6

A rectangular loop has sides of length 0.06 m and 0.08 m. The wire carries a current of 10 A in the direction shown. The loop is in a uniform magnetic field of magnitude 0.2 T and directed in the positive x direction. What is the magnitude of the torque on the loop?

8 × 10–3 N × m

)sin( NIAB

Magnetism7

A solenoid of length 0.250 m and radius 0.0250 m is comprised of 440 turns of wire. Determine the magnitude of the magnetic field at the center of the solenoid when it carries a current of 12.0 A.

2.21 × 10–3 T

Magnetism8

The drawing shows two long, thin wires that carry currents in the positive z direction. Both wires are parallel to the z axis. The 50-A wire is in the x-z plane and is 5 m from the z axis. The 40-A wire is in the y-z plane and is 4 m from the z axis. What is the magnitude of the magnetic field at the origin?

3 × 10–6 T

(exact) 104

2

70

0

A

Tm

r

IB

Magnetism9

Moving On to the next chapter……………….

I

I

INTRODUCTION TO INDUCTION

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10

Induction

Important Definition – Magnetic Flux

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11

AREA

Magnetic Field

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The Essence of this Topic

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13

Consider a conductor that is shaped in a loop but is continuous.

The conductor has a magnetic field through the loop that is not necessarily uniform.

There is a MAGNETIC FLUX through this loop. If the FLUX CHANGES, an “emf” will be

induced around the loop. This emf can cause a current to flow around

the loop.

How Can You Change the Magnetic Flux Going Through The Loop? Huh?

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14

Divide the area of the loop into a very large number of small areas A.

Find the Magnetic Field through each area as well as the angle that it makes with the normal to the area.

Compute the total flux through the loop.

The Magnetic Flux Going Through The Loop:

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15

iii

i AB )cos(

Add up all of these piecesthat are INSIDE the loop.

Changing

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16

Change any or all of the Bi

i

Change the SHAPE of the loop Change the ANGLE that the loop

makes with the magnetic field (subset of above)

And the Flux will change!ii

ii AB )cos(

WAIT A SECOND …….

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17

You said that there is a conducting loop. You said that there is therefore a

VOLTAGE or emf around the loop if the flux through the loop changes.

But the beginning and end point of the loop are the same so how can there be a voltage difference around the loop?

‘tis a puzzlement!

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REMEMBER when I said E Fields start and end on CHARGES???

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19

DID I LIE??

The truth

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20

Electric fields that are created by static charges must start on a (+) charge and end on a (–) charge as I said previously.

Electric Fields created by changing magnetic fields can actually be shaped in loops.

Why do you STILL think I am a liar?

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21

Because you said that an emf is a

voltage so if I put a voltmeter from one point on the loop

around to the same point, I will get

ZERO volts, won’t I

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The POTENTIAL between two points

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23

Is the WORK that an external agent has to do to move a unit charge from one point to another.

But we also have (neglecting the sign): sEV

s

So, consider the following:

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24

E

Conductor

x x x x x x xx x x x x x xx x x x x x xx x x x x x xx x x x x x xx x x x x x x

zeroREemf

sEsEemf

2

THEREFORE WHAT WILL A VOLTMETER READ FROM A to A?

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25

E

Conductor

x x x x x x xx x x x x x xx x x x x x xx x x x x x xx x x x x x xx x x x x x x

A

A The emfB ZeroC Can’t tell

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26

temf loopthe

Through

Michael Faraday (1791-1867)

MINUS????

A: The way that you don’t want it to point! (Lenz’s Law).

Lenz’s Law Explains the (-) sign!

Q: Which way does E point?

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Induction

OK. LET’S DO THE PHYSICS NOW

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Induction

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Is there an induced current???

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30

Induction Effects

Faraday’s Experiments

??

Insert Magnet into Coil

Remove Coil from Field Region

Summary

Does the Flux Change?

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36

In the Previous Example, if there are N coils rather than a single coil,

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37

A The current is increased by a factor of NB The current is decreased by a factor of NC The current stays the same.

Push a magnet into a coil of two wires and a current is produced via an emf.

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In this case, 2 coils, each has the SAME emf.

Ohm’s Law still works, so

coilR

emfi

tNemf

If we go from 2 to 4 coils, the current

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A Stays the sameB DoublesC Is halvedD Is four times larger

A rectangular circuit containing a resistor is perpendicular to a uniform magnetic field that starts out at 2.65 T and steadily decreases at 0.25 T/s. While this field is changing, what does the ammeter read?

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40

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••The conducting rod ab shown makes frictionless contact with metal rails ca and db. The apparatus is in a uniform magnetic field of 0.800 T, perpendicular to the plane of the figure. (a) Find the magnitude of the emf induced in the rod when it is moving toward the right with a speed 7.50 m/s.

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tABemf sin

Almost DC

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43

THE STRANGE WORLD OF DR. LENTZ

LENZ’S LAWInduced Magnetic Fields always FIGHT to stop what you are trying to do!i.e... Murphy’s Law for Magnets

Example of Nasty Lenz

The induced magnetic field opposes thefield that does the inducing!

Don’t Hurt Yourself!

The current i induced in the loop has the directionsuch that the current’s magnetic field Bi opposes thechange in the magnetic field B inducing the current.

Let’s do theLentz Warp

again !

Again: Lenz’s Law

An induced current has a directionsuch that the magnetic field due tothe current opposes the change in the magnetic flux that induces thecurrent. (The result of the negative sign that we always leave out!) …

OR

The toast will always fall buttered side down!

What Happens Here?

Begin to move handle as shown. Assume a resistance R in the loop.

Flux through the loop decreases.

Current is induced which opposed this decrease – current tries to re-establish the B field.

What about a SOLID loop??

METAL Pull

Energy is LOSTBRAKING SYSTEM

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A cardboard tube is wrapped with two windings of insulated wire, as shown. Is the induced current in the resistor R directed from left to right or from right to left in the following circumstances?

The current in winding A is directed

(a) from a to b and is increasing,

(b) from b to a and is decreasing,

(c) from b to a and is increasing, and

(d) from b to a and is constant.

left right

Mutual inductance –

Circulation of currents in one coil can generate a field in the coil that will extend to a second, close by device.

Suppose i1 CHANGES

Flux Changes

Current (emf) isinduced in 2nd

coil.

The two coils

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55

Remember – the magneticfield outside of the solenoidis pretty much zero.

Two fluxes (fluxi?) are the same!Two fluxes (fluxi?) are the same!

Self-inductance –

Any circuit which carries a varying current self-induced from it’s own magnetic field is said to

have INDUCTANCE (L).

An inductor resists CHANGESCHANGES in the current going through it.

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An inductor resists CHANGESCHANGES in the current going through it.

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An inductor resists CHANGESCHANGES in the current going through it.

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Inductance Defined

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60

i

NL B

If the FLUX changes a but during a short time t, then the current will change by a small amount i.

t

iL

tN

NLi

B

B

This is actually acalculus equation

Faraday says this is the emf!

So …

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61

t

iLemf

E=

The UNIT of “Inductance – L” of a coil is the henry.

SYMBOL:

There should bea (-) sign but weuse Lenz’s Lawinstead!

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Consider “AC” voltage

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63

V1

Maximum Change/t

Minimum Change/t

The transformer

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FLUX is the same throughboth coils (windings). 2

2

1

1

222

111

N

V

N

V

tNVemf

tNVemf

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Input/Output Impedance (Resistance)

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67

!resistance

inputan like looks

)/(

(Lossless)

2121

1

2211

1

2

1

2

NN

R

I

V

So

VIVI

PowerPower

N

N

V

V

outin

Read in the textbook section 21.10:

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68

0

2

2B

VolumeUnit

Energyu

Energy associated with an induced current.

As energy is introduced at induces a field, energy is stored in an electronic device. Refer to worked example 21.12 in your text.

The R-L circuit – Figure 21.29 When an inductor is part of a wired circuit, - voltages, currents and capacitor charges are a function of time, not constants. Refer to worked example 21.13 in your text.

The L-C circuit – Figure 21.34 When an inductor is part of a wired circuit with a capacitor, the capacitor charges over time. Commonly used in radio as a tuner for the induced current from an antenna.