part b - magnetism

7/28/2019 Part B - Magnetism

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Part 2: Magnetism

Chapter 4: Magnets , magnetic field, magnetic field lines and magnetic force

4.1. Ferromagnets and Electromagnets

4.2. Magnetic Fields and Magnetic Field Lines

4.3. Magnetic Field Strength: Force on a Moving Charge in a Magnetic

4.4. Force on a Moving Charge in a Magnetic Field: Examples and Applications

4.5. The Hall EffectChapter 5: Ampere Law & Magnetic Force

5.1. Magnetic Force on a Current-Carrying Conductor

5.2. Torque on a Current Loop: Mot ors and Meters

5.3. Magnetic Force between Two Parallel Conductors

5.4. Magnetic Fields Produced by Currents: Amperes Law

Chapter 6: Electromagnetic induction

6.1. Electromagnetic induction

6.2. Faradays Law

6.3. L enzs Law

6.4. More Applications of Magnetism

Chapter 4Chapter 4

Chapter 4: Mangetism 4.1. Magnets

FerromagnetsFerromagnets


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Properties of magnetsProperties of magnets

If a material is magnetic, it has the ability toexert forces on magnets or other magneticmaterials nearby.

A permanent magnet is a material that keepsits magnetic properties.


Properties of MagnetsProperties of Magnets

All magnets have two

opposite magnetic

poles, called the north

pole and south pole.

If a magnet is cut in

half, each half will

have its own north

and south poles.


Properties of magnetsProperties of magnets

Whether the two magnets attract or repel

depends on which poles face each other.


Magnetic forceMagnetic force


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Magnetic forces can pass through many

materials with no apparent decrease in

strength.



Magnetic forces are used

in many applications

because they are relativelyeasy to create and can be

very strong.

Large magnets, such as

this electromagnet, create

forces strong enough to lift

a car or a moving train.


Magnetic fieldMagnetic field

Reminder: electric field surrounds electric charge

Magnetic field surrounds any moving

electric charge (current)Magnetic field surrounds a magnetic

material (permanent magnet)


Magnetic fieldMagnetic field

A vector quantity, Symbolized by

Direction is given by the direction a north pole of a compass needle

Magnetic field lines show how the field lines, as traced out by a compass

B

B


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How a magnetic field affects another magnetHow a magnetic field affects another magnet

Magnets A and C feel a net attracting force toward the source magnet.

Magnets B and D feel a twisting force, or torque, because one pole is repelled

and the opposite pole is attracted with approximately the same strength.


Magnetic Field Lines, Bar MagnetMagnetic Field Lines, Bar Magnet

The compass can be used

to trace the field lines

The lines outside the

magnet point from theNorth pole to the South

pole


Magnetic Field Lines, Bar MagnetMagnetic Field Lines, Bar Magnet

Iron filings are used to

show the pattern of the

electric field lines

The direction of the field

is the direction a north

pole would point


Magnetic Field Lines, Unlike PolesMagnetic Field Lines, Unlike Poles



electric field lines

The direction of the field


pole would point Compare to the electric

field produced by an

electric dipole


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Magnetic Field Lines, Like PolesMagnetic Field Lines, Like Poles



electric field lines The direction of the field


pole would point

Compare to the electric

field produced by like

charges


Magnets and Magnetic FieldsMagnets and Magnetic Fields

A uniform magnetic field is constant inmagnitude and direction.

The field between

these two wide poles

is nearly uniform.

Chapter 4Chapter 4


A long and straight wire

creates field lines forming

circular loops


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a circular current loop is

similar to that of a bar magnet



Magnetism in materialsMagnetism in materials

Electron orbits a nucleus aclosed-current loop producing a

magnetic field with a north pole

and a south pole like a tiny magnet

Electrons have spin forming acurrent produces a magnetic

field with a north pole and a south

pole like a tiny magnet

Atoms act like tiny magnetswith north and south poles.



Atoms act like tinymagnets with north andsouth poles.

When permanent

magnets have theiratoms aligned, weobserve the magneticforces.

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In many materials, the magnetic fields ofindividual electrons in each atom canceleach others magnetic effects.

Lead and diamond are materials made ofthese kinds of atoms and are calleddiamagnetic.

It takes either a very strong magnetic field tocause the effects or very sensitiveinstruments to detect them.



Aluminum is paramagnetic.

In an atom of aluminum, themagnetism of individualelectrons do not cancel

completely. This makes each aluminum

atom a tiny magnet with anorth and a south pole.

Solid aluminum isnonmagnetic because thetotalmagnetic field averages tozero.


Nonmagnetic materialsNonmagnetic materials

The atoms in non-magnetic materials,like plastic, are notfree to move orchange their magneticorientation.


Magnetic materialsMagnetic materials

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Ferromagnetic materialsFerromagnetic materials

A small group of ferromagnetic

metals have very strong

magnetic properties: Fe, Co, Ni.

Atoms in ferromagnetic

materials align themselves with

neighboring atoms in groups

called magnetic domains.


Magnetism in solidsMagnetism in solids

If you use the north end of the

magnet to pick up a nail, the nail

becomes magnetized with its south

pole toward the magnet.

Because the nail itself becomes a

magnet, it can be used to pick up

other nails.

If you separate that first nail from

the bar magnet, the entire chain

demagnetizes and falls apart.


Force on a Moving Charge in a Magnetic FieldForce on a Moving Charge in a Magnetic Field



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EE--field and Bfield and B--fieldfield


Motion of A Point Charge in Magnetic FieldMotion of A Point Charge in Magnetic Field

v

B

F



B

-q

F

velocity component v B

circular motion

Cyclotron Period

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= v//T

r



when a magnet comes in contact with a computer monitor or TV screen: Electrons moving toward

the screen spiral about magnetic field lines, maintaining the component of their velocity parallel to

the field lines. This distorts the image on the screen.



When a charged particle moves along a magnetic field line into a region where the field

becomes stronger, the particle experiences a force that reduces the component of

velocity parallel to the field. This force slows the motion along the field line and here

reverses it


Hall effectHall effect

HV EW

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BALANCE

HV EW BW v

VH is Hall effect voltage across conductor of width W and charges move at a speed v



Applications: Measurement of magnetic field strength B

Hall probes

i nqAdv

i

nqA

dv

i

nqA

dv

HVBW

d

with A = Width (W)x thickness (t)

HV BW dw

t

H

nqtB V

i


Magnetic Force on CurrentsMagnetic Force on Currents

Current = many charges moving together

Total number offorce on one charge carrier

charge carrier

.d

F q B n A L

v

i nqAd

v

F i L B

direction of is the direction of currentdL

v

For an small segment dl

d F i dl B

sinF ilB

sind F i dl B



Right Hand Rule 1 (RHR-1)

The thumb in the direction of the current I

The fingers in the direction ofB ,

=> perpendicular to the palm points in the

direction ofF

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Example 1

Force on a semicircle current loop

d F i d l B

, 90dF idlB dl B

d F i dl B

zSymmetry consider vertical forces sindF dF

z

0

Total Force:

sin sinF dF dF iB dl iBR d

2F iBR (downward)



Example 1

Current loop in B-field

=> applications: Motor, Generator



Multiple loop of N turns, we get

N times the torque of one loop



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Magnetic Force on CurrentsMagnetic Force on CurrentsUnit vector to represent the area-vecto (using right hand rule)n



As the angular momentum of the

coil carries it through = 0

The current reversing each half revolution

to maintain the clockwise torque.

Applications: Motors


Magnetic Force on CurrentsMagnetic Force on CurrentsApplications: Motors


Magnetic Force on CurrentsMagnetic Force on CurrentsApplications: Meters Similar to motors but only rotate through a part of a

revolution => Deflection against the return spring is

proportional current I

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Magnetic FieldMagnetic Field


Magnetic Field due to moving chargeMagnetic Field due to moving charge


Magnetic FieldMagnetic Field

charges => E-field

Currents => B-field


Magnetic Field due to current segmentsMagnetic Field due to current segments

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Magnetic FieldMagnetic FieldCreated by a Long Straight Current-Carrying Wire: Right Hand Rule 2


Electric & MagneticElectric & Magnetic

Electric Magnetic

Basic element dq

E/B-field Coulomb's Law: Biot-Savart Law

Electric/Magnetic

Dipole

Torque

id s

2e

dqd E k r

r

2m

id s r d B k

r

eP qd

mP iAn

e eP E

e m

P B


Calculation of magnetic fieldCalculation of magnetic fieldExample 1 : Magnetic field due to straight current segment

I

d z

aP

o 1 2cos cos4

IB

a

1

2

Special case:

Infinitely long, straight wire

o

2

IB

a


Calculation of magnetic fieldCalculation of magnetic fieldExample 2 : Magnetic field at point O due to current wire segment

ds Rd

o

4B

R

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Calculation of magnetic fieldCalculation of magnetic fieldExample 3 : Magnetic field on the axis of a Circular current loop

R

I

2

o

3/ 22 2

2

iRB

R z

Direction determined from right-hand rule

Limiting Cases :

(1) At center of loop

2

o

2

iRB

R

(2) For z >> R

2

o

32

iRB

z

2

o

32

iRB

r



R

I

2

o

3/ 22 2

2

iRB

R z

Direction determined from right-hand rule

Limiting Cases :

(1) At center of loop

o

2

iB

R

(2) For z >> R

2

o

32

iRB

z

o

3 3

1~

2

iAB

z



Field line pattern likes around

bar magneti

Field line pattern around

circular current


Calculation of magnetic fieldCalculation of magnetic fieldExample 4 : Magnetic field produced by a solenoid

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Calculation of magnetic fieldCalculation of magnetic fieldExample 4 : Magnetic field produced by a solenoid

( )


Magnetic force between Parallel currentsMagnetic force between Parallel currents

A current produces magnetic field

Magnetic force acts on a current

=> Two current exert magnetic forces on eac h other

=> Force on wire 1

d F i d l B

Currents in same directions repulsive each other

Currents in opposite directions repel each other

=> Force per unit length


Gausss LawGausss Law

ind A q

???Bd A

0There is no magnetic monopole


Amperes LawAmperes Law

No current is present in the

wire, all the needles point in the

same direction

(Earths magnetic field)

The wire carries a strong, the

needles all deflect in a direction

tangent to the circle

?C

Bds

0

C

Bd s

oC

Bd s i

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Amperes LawAmperes Law

1

N

i

C

Bd s i

1 4C

Bds i i


Amperes Law ApplicationsAmperes Law Applications

Rectangular path: the field along the length

inside the coil is the dominant contribution

and the other parts is negligible.

rectangular

path

1

N

i

C

Bds i

Amperes L aw

0

l

Bds Ni

0

l

B ds nli

Constant field:

(n density of turns)

B ni 70 4 10 T/Am



Magnetic along the straight wire

r

1

N

i

C

Bd s i

Amperes Law

2

0

r

Bds i

2B r i

2

iB

r

70 4 10 T/Am



Magnetic Field of Toroid

Circular path

1

N

i

C

Bd s i

Amperes L aw

2

0

r

Bds Ni

2B r Ni

2

NiB

r

70 4 10 T/Am

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Chapter 6Chapter 6


ExperimentsExperiments



Movement of a magnet relative to a coil produces emfs as shown.

The same emfs are produced if the coil is moved relative to the magnet.

The greater the speed, the greater the magnitude of the emf

The emf is zero when there is no motion


ExperimentsExperimentsElectric generator

Rotate a coil in a magnetic field = >

produces an emf.

Mechanical energy done is converted to

electric energy.

Note the generator is very similar in

construction to a motor

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cosd Bd A BdA

Magnetic flux, , given by

B - magnetic field strength over an area A

angle between the pe rpendicular to the

area and B


Faradays law of inductionFaradays law of induction

Bd

dt

The emf induced in a circuit is directly proportional to the time

rate of change of the magnetic flux through the circuit

Faradays law of induction

If the circuit is a coil consisting of N loops

BdNdt

cosd BA

dt

By changing:

Magnitude of B

Area enclosed by the loop

Angle between B and normal of the


Lenzs lawLenzs law

Thepolarityof theinduced

emf is suchthatit tends to

pr odu ce a cu rre nt t hat

creates a magnetic flux to

oppose the change in

magnetic flux through thearea enclosed by the

currentloop


Faradays law applicationsFaradays law applications

The ground fault interrupter (GFI)

safety device protects users of

electrical appliances against

electric shock

Two currents 1 and 2 are opposite directions

=> net magnetic flux is zero

If appliance gets wet, current leak to ground

the return current 2 changes the net magnetic flux is no longer zero

inducing an emf in the coil

Trigger breaker stopping current before

harmful level

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Production of sound in an electric guitar

Pickup coil placed near the vibrating guitar string can be magnetized.

A permanent magnet inside the coil magnetizes the portion of the string nearest the coil.

When the string vibrates at some frequency, the magnetized segment produces a

changing magnetic flux in the coil => Induces an emf in the coil that is fed to an amplifier.

The output of the amplifier is sent to the loudspeakers producing the sound wave



Generators

AC generator consists of a coil - or coils - of wire moving relative to a

magnetic field. With this arrangement, a voltage is induced and this

generates a current in a circuit.

In a bicycle dynamo, a magnet turns

inside a coil of wire when the back

wheel of the bicycle is turning.



Transformers

Transformers are used to change

the size of an ac voltage.

The secondary voltage depends on

the number of turns on both the

primary and the secondary coils and

on the voltage across primary coil.

s s

p p

V V

V V

Vs is the voltage induced in the secondary coil in volts

Vp is the voltage applied to the primary coil in volts

ns is the number of turns on the secondary coil

np is the number of turns on the primary coil

part b - magnetism

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