Magnetism

Содержание

Слайд 2

Magnetism A Whole New Topic

Magnetism

A Whole New Topic

Слайд 3

DEMO

DEMO

Слайд 4

Magnetism Lodestone (Mineral) Lodestones attracted iron filings. Lodestones seemed to attract

Magnetism

Lodestone (Mineral)

Lodestones attracted iron filings.
Lodestones seemed to attract each other.
Used as

a compass.
One end always pointed north.
Lodestone is a natural magnet.
Слайд 5

Magnetism Magnetism Refrigerators are attracted to magnets!

Magnetism

Magnetism

Refrigerators are attracted to magnets!

Слайд 6

Magnetism Applications Motors Navigation – Compass Magnetic Tapes Music, Data Television

Magnetism

Applications

Motors
Navigation – Compass
Magnetic Tapes
Music, Data
Television
Beam deflection Coil
Magnetic Resonance Imaging
High Energy Physics

Research
Слайд 7

Magnetism Magnets Like Poles Repel Opposite Poles Attract Magnetic Poles are

Magnetism

Magnets

Like Poles Repel
Opposite Poles Attract
Magnetic Poles are only found in pairs.
No

magnetic monopoles have ever been observed.

Shaded End is NORTH Pole
Shaded End of a compass points
to the NORTH.

S N

Слайд 8

Magnetism Observations Bring a magnet to a charged electroscope and nothing

Magnetism

Observations

Bring a magnet to a charged electroscope and nothing happens. No

forces.
Bring a magnet near some metals (Co, Fe, Ni …) and it will be attracted to the magnet.
The metal will be attracted to both the N and S poles independently.
Some metals are not attracted at all.
Wood is NOT attracted to a magnet.
Neither is water.
A magnet will force a compass needle to align with it. (No big Surprise.)
Слайд 9

Magnetism Magnets Cutting a bar magnet in half produces TWO bar

Magnetism

Magnets

Cutting a bar magnet in half produces TWO bar magnets,

each with N and S poles.

Magnetic Field

Слайд 10

Magnetism Consider a Permanent Magnet

Magnetism

Consider a Permanent Magnet

Слайд 11

Magnetism Introduce Another Permanent Magnet The bar magnet (a magnetic dipole)

Magnetism

Introduce Another Permanent Magnet

The bar magnet (a magnetic dipole) wants to

align with the B-field.

pivot

Слайд 12

Magnetism The south pole of the small bar magnet is attracted

Magnetism

The south pole of the small bar magnet is attracted towards

the north pole of the big magnet.
Also, the small bar magnet (a magnetic dipole) wants to align with the B-field.
The field attracts and exerts a torque on the small magnet.

Field of a Permanent Magnet

Слайд 13

Magnetism Field of a Permanent Magnet The field exerts a torque

Magnetism

Field of a Permanent Magnet

The field exerts a torque on the

dipole

The bar magnet (a magnetic dipole) wants to align with the B-field.

Слайд 14

Magnetism The Magnetic Field Similar to Electric Field … exists in

Magnetism

The Magnetic Field

Similar to Electric Field … exists in space.
Has Magnitude

AND Direction.
The “stronger” this field, the greater is the ability of the field to interact with a magnet.
Слайд 15

Magnetism Convention For Magnetic Fields X  Field INTO Paper Field OUT of Paper B

Magnetism

Convention For Magnetic Fields

X 
Field INTO Paper Field OUT of

Paper

B

Слайд 16

Magnetism Experiments with Magnets Show Current carrying wire produces a circular

Magnetism

Experiments with Magnets Show

Current carrying wire produces a circular magnetic field

around it.
Force on Compass Needle (or magnet) increases with current.
Слайд 17

Magnetism Current Carrying Wire Current into the page. Right hand Rule-

Magnetism

Current Carrying Wire

Current into
the page.

Right hand Rule-
Thumb in direction of the

current
Fingers curl in the direction of B
Слайд 18

Magnetism Current Carrying Wire B field is created at ALL POINTS

Magnetism

Current Carrying Wire

B field is created at ALL POINTS in space

surrounding the wire.
The B field had magnitude and direction.
Force on a magnet increases with the current.
Force is found to vary as ~(1/d) from the wire.
Слайд 19

Magnetism Compass and B Field Observations North Pole of magnets tend

Magnetism

Compass and B Field

Observations
North Pole of magnets tend to move toward

the direction of B while S pole goes the other way.
Field exerts a TORQUE on a compass needle.
Compass needle is a magnetic dipole.
North Pole of compass points toward the NORTH.
Слайд 20

Magnetism Planet Earth

Magnetism

Planet Earth

Слайд 21

Magnetism Inside it all. 8000 Miles

Magnetism

Inside it all.

8000
Miles

Слайд 22

Magnetism On the surface it looks like this..

Magnetism

On the surface it looks like this..

Слайд 23

Magnetism Inside: Warmer than Floriduh

Magnetism

Inside: Warmer than Floriduh

Слайд 24

Magnetism Much Warmer than Floriduh

Magnetism

Much Warmer than Floriduh

Слайд 25

Magnetism Finally

Magnetism

Finally

Слайд 26

Magnetism In Between The molten iron core exists in a magnetic

Magnetism

In Between

The molten iron core exists in a magnetic field that

had been created from other sources (sun…).
The fluid is rotating in this field.
This motion causes a current in the molten metal.
The current causes a magnetic field.
The process is self-sustaining.
The driving force is the heat (energy) that is generated in the core of the planet.
Слайд 27

Magnetism After molten lava emerges from a volcano, it solidifies to

Magnetism

After molten lava emerges from a volcano, it solidifies to a

rock. In most cases it is a black rock known as basalt, which is faintly magnetic, like iron emerging from a melt. Its magnetization is in the direction of the local magnetic force at the time when it cools down.
Instruments can measure the magnetization of basalt. Therefore, if a volcano has produced many lava flows over a past period, scientists can analyze the magnetizations of the various flows and from them get an idea on how the direction of the local Earth's field varied in the past. Surprisingly, this procedure suggested that times existed when the magnetization had the opposite direction from today's. All sorts of explanation were proposed, but in the end the only one which passed all tests was that in the distant past, indeed, the magnetic polarity of the Earth was sometimes reversed.
Слайд 28

Magnetism Ancient Navigation

Magnetism

Ancient Navigation

Слайд 29

Magnetism This planet is really screwed up! NORTH POLE SOUTH POLE

Magnetism

This planet is really screwed up!

NORTH
POLE

SOUTH POLE

Слайд 30

Magnetism Repeat Navigation DIRECTION N S If N direction is pointed

Magnetism

Repeat

Navigation
DIRECTION
N
S

If N direction
is pointed to by
the NORTH pole
of the Compass
Needle,

then the
pole at the NORTH
of our planet must
be a SOUTH MAGNETIC
POLE!

And it REVERSES from time to time.

Слайд 31

Magnetism

Magnetism

Слайд 32

Magnetism Rowland’s Experiment Rotating INSULATING Disk which is CHARGED + or

Magnetism

Rowland’s Experiment

Rotating
INSULATING
Disk
which is
CHARGED
+ or –
on exterior.

xxx
xxx B
xxx

Field is created by
any

moving charge.
Increases with
charge on the
disk.
Increases with
angular velocity of
the disk.
Electrical curent is a
moving charge.

++
+ + ++

Слайд 33

Magnetism A Look at the Physics There is NO force on

Magnetism

A Look at the Physics

There is NO force on
a charge placed

into a
magnetic field if the
charge is NOT moving.

There is no force if the charge
moves parallel to the field.

Слайд 34

Magnetism WHAT THE HECK IS THAT??? A WHAT PRODUCT? A CROSS

Magnetism

WHAT THE HECK IS THAT???

A WHAT PRODUCT?
A CROSS PRODUCT – Like

an angry one??
Alas, yes ….
F=qv X B
Слайд 35

Magnetism The Lorentz Force This can be summarized as: v F

Magnetism

The Lorentz Force

This can be summarized as:

v

F

B

q

m

or:

θ is the angle between

B and V
Слайд 36

Magnetism Note B is sort of the Force per unit (charge-velocity) Whatever that is!!

Magnetism

Note

B is sort of the Force per unit (charge-velocity)
Whatever that is!!

Слайд 37

Magnetism Practice Which way is the Force??? B and v are

Magnetism

Practice

Which way is the Force???

B and v are parallel.
Crossproduct is zero.
So

is the force.
Слайд 38

Magnetism Units

Magnetism

Units

Слайд 39

Magnetism teslas are HUGE!

Magnetism

teslas are

HUGE!

Слайд 40

Magnetism The Magnetic Force is Different From the Electric Force. Whereas

Magnetism

The Magnetic Force is Different From the Electric Force.

Whereas the electric

force acts in the same direction as the field:

The magnetic force acts in a direction orthogonal to the field:

And --- the charge must be moving !!

(Use “Right-Hand” Rule to
determine direction of F)

Слайд 41

Magnetism So… A moving charge can create a magnetic field. A

Magnetism

So…

A moving charge can create a magnetic field.
A moving charge is

acted upon by a magnetic field.
In Magnetism, things move.
In the Electric Field, forces and the field can be created by stationary charges.
Слайд 42

Magnetism Trajectory of Charged Particles in a Magnetic Field + +

Magnetism

Trajectory of Charged Particles in a Magnetic Field

+ + + +
+ + + +
+ + + +
+ + + +
+ + + +

v

B

F

(B field points into plane

of paper.)
Слайд 43

Magnetism Trajectory of Charged Particles in a Magnetic Field + +

Magnetism

Trajectory of Charged Particles in a Magnetic Field

+ + + +
+ + + +
+ + + +
+ + + +
+ + + +

+ + + +
+ + + +
+ + + +
+ + + +
+ + + +

v

v

B

B

F

F

(B field points into plane

of paper.)

Magnetic Force is a centripetal force

Слайд 44

Magnetism Review of Rotational Motion

Magnetism

Review of Rotational Motion

Слайд 45

Magnetism YES ! You have to remember this stuff.

Magnetism

YES ! You have to remember this stuff.

Слайд 46

Magnetism + + + + + + + + + +

Magnetism

+ + + +
+ + + +
+ + + +
+ + + +
+ + + +

Radius of a Charged Particle Orbit in a Magnetic Field

v

B

F

r

Centripetal Magnetic
Force

Force

=

Слайд 47

Magnetism Cyclotron Frequency The time taken to complete one orbit is: V cancels !

Magnetism

Cyclotron Frequency

The time taken to complete one
orbit is:

V cancels !

Слайд 48

Magnetism More Circular Type Motion in a Magnetic Field

Magnetism

More Circular Type Motion in a Magnetic Field

Слайд 49

Magnetism Mass Spectrometer

Magnetism

Mass Spectrometer

Слайд 50

Magnetism

Magnetism

Слайд 51

Magnetism Cyclotron Frequency The time taken to complete one orbit is: V cancels !

Magnetism

Cyclotron Frequency

The time taken to complete one
orbit is:

V cancels !

Слайд 52

Magnetism An Example A beam of electrons whose kinetic energy is

Magnetism

An Example

A beam of electrons whose kinetic energy is K emerges

from a thin-foil “window” at the end of an accelerator tube. There is a metal plate a distance d from this window and perpendicular to the direction of the emerging beam. Show that we can prevent the beam from hitting the plate if we apply a uniform magnetic field B  such that
Слайд 53

Magnetism Problem Continued

Magnetism

Problem Continued

Слайд 54

Some New Stuff Magnetism and Forces

Some New Stuff

Magnetism and Forces

Слайд 55

Magnetism Let’s Look at the effect of crossed E and B

Magnetism

Let’s Look at the effect of crossed E and B Fields:

x

x

x

x

x

x

•

q

, m

B

v

E

Слайд 56

Magnetism What is the relation between the intensities of the electric

Magnetism

What is the relation between the intensities of the electric and


magnetic fields for the particle to move in a straight line ?.

FE = q E and FB = q v B

If FE = FB the particle will move
following a straight line trajectory

q E = q v B

Слайд 57

Magnetism What does this mean?? This equation only contains the E

Magnetism

What does this mean??

This equation only contains the E and B

fields in it.
Mass is missing!
Charge is missing!
This configuration is a velocity filter!
Слайд 58

Magnetism “Real” Mass Spectrometer Create ions from injected species. This will

Magnetism

“Real” Mass Spectrometer

Create ions from injected species.
This will contain various masses,

charges and velocities.
These are usually accelerated to a certain ENERGY (KeV) by an applied electric field.
The crossed field will only allow a selected velocity to go forward into the MS.
From before: R=mv/Bq
Слайд 59

Magnetism Components of MS:

Magnetism

Components of MS:

Слайд 60

Magnetism Remember: THESE "E and B" GUYS ARE VECTORS! Let's Look at an example...

Magnetism

Remember: THESE "E and B" GUYS ARE VECTORS!

Let's Look at an

example...
Слайд 61

Magnetism VECTOR CALCULATIONS

Magnetism

VECTOR CALCULATIONS

Слайд 62

Magnetism Problem: A Vector Example A proton of charge +e and

Magnetism

Problem: A Vector Example

A proton of charge +e and mass m

is projected into a uniform magnetic field B=Bi with an initial velocity v=v0xi +v0yj. Find the velocity at a later time.

vx is constant

Слайд 63

Magnetism More

Magnetism

More

Слайд 64

Magnetism New Topic Forces on Wires

Magnetism

New Topic Forces on Wires

Слайд 65

Magnetism Wires A wire with a current contains moving charges. A

Magnetism

Wires

A wire with a current contains moving charges.
A magnetic field will

apply a force to those moving charges.
This results in a force on the wire itself.
The electron’s sort of PUSH on the side of the wire.

F

Remember: Electrons go the “other way”.

Слайд 66

Magnetism The Wire in More Detail B out of plane of

Magnetism

The Wire in More Detail

B out of plane of the paper

Assume

all electrons are moving
with the same velocity vd.
Слайд 67

Magnetism Magnetic Levitation mg Where does B point???? Into the paper.

Magnetism

Magnetic Levitation

mg

Where does B point????

Into the paper.

Слайд 68

Magnetism MagLev

Magnetism

MagLev

Слайд 69

Magnetism Magnetic Repulsion

Magnetism

Magnetic Repulsion

Слайд 70

Magnetism Detail

Magnetism

Detail

Слайд 71

Magnetism Moving Right Along ….

Magnetism

Moving Right Along ….

Слайд 72

Magnetism Acceleration

Magnetism

Acceleration

Слайд 73

Magnetism Don’t Buy A Ticket Quite Yet.. This is still experimental.

Magnetism

Don’t Buy A Ticket Quite Yet..

This is still experimental.
Much development still

required.
Some of these attempts have been abandoned because of the high cost of building a MagLev train.
Probably 10-20 years out.
Or More.
Слайд 74

Magnetism Current Loop Loop will tend to rotate due to the

Magnetism

Current Loop

Loop will tend to rotate due to the torque the

field applies to the loop.
Слайд 75

Magnetism The Loop OBSERVATION Force on Side 2 is out of

Magnetism

The Loop

OBSERVATION
Force on Side 2 is out
of the paper and that

on
the opposite side is into
the paper. No net force
tending to rotate the loop
due to either of these forces.
The net force on the loop is
also zero,
Слайд 76

Magnetism An Application The Galvanometer

Magnetism

An Application The Galvanometer

Слайд 77

Magnetism The other sides τ1=F1 (b/2)Sin(θ) =(B i a) x (b/2)Sin(θ)

Magnetism

The other sides

τ1=F1 (b/2)Sin(θ)
=(B i a) x (b/2)Sin(θ)
total torque on


the loop is: 2τ1
Total torque:
τ=(iaB) bSin(θ)
=iABSin(θ)
(A=Area)
Слайд 78

Magnetism Watcha Gonna Do Quiz Today Return to Magnetic Material Exams not yet returned. Sorry.

Magnetism

Watcha Gonna Do

Quiz Today
Return to Magnetic Material
Exams not yet returned. Sorry.

Слайд 79

Magnetism Wires A wire with a current contains moving charges. A

Magnetism

Wires

A wire with a current contains moving charges.
A magnetic field will

apply a force to those moving charges.
This results in a force on the wire itself.
The electron’s sort of PUSH on the side of the wire.

F

Remember: Electrons go the “other way”.

Слайд 80

Magnetism The Wire in More Detail B out of plane of

Magnetism

The Wire in More Detail

B out of plane of the paper

Assume

all electrons are moving
with the same velocity vd.
Слайд 81

Magnetism Current Loop Loop will tend to rotate due to the

Magnetism

Current Loop

Loop will tend to rotate due to the torque the

field applies to the loop.
Слайд 82

Magnetism Last Time τ1=F1 (b/2)Sin(θ) =(B i a) x (b/2)Sin(θ) total

Magnetism

Last Time

τ1=F1 (b/2)Sin(θ)
=(B i a) x (b/2)Sin(θ)
total torque on
the

loop is: 2τ1
Total torque:
τ=(iaB) bSin(θ)
=iABSin(θ)
(A=Area)
Слайд 83

Magnetism A Coil Normal to the coil RIGHT HAND RULE TO

Magnetism

A Coil

Normal to the
coil

RIGHT HAND RULE TO FIND NORMAL TO THE COIL:
“Point

or curl you’re the fingers of your right
hand in the direction of the current and your
thumb will point in the direction of the normal
to the coil.

Don't hurt yourself doing this!

Слайд 84

Magnetism Dipole Moment Definition Define the magnetic dipole moment of the

Magnetism

Dipole Moment Definition

Define the magnetic
dipole moment of
the coil μ as:
=NiA
We can

convert this
to a vector with A
as defined as being
normal to the area as
in the previous slide.
Слайд 85

Magnetism Current Loop

Magnetism

Current Loop

Слайд 86

Magnetism A length L of wire carries a current i. Show

Magnetism

A length L of wire carries a current i. Show that

if the wire is formed into a circular coil, then the maximum torque in a given magnetic field is developed when the coil has one turn only, and that maximum torque has the magnitude … well, let’s see.
Слайд 87

Magnetism Problem continued…

Magnetism

Problem continued…

Слайд 88

Magnetism Energy

Magnetism

Energy

Слайд 89

The Hall Effect

The Hall Effect

Слайд 90

Magnetism What Does it Do? Allows the measurement of Magnetic Field

Magnetism

What Does it Do?

Allows the measurement of Magnetic Field if a

material is known.
Allows the determination of the “type” of current carrier in semiconductors if the magnetic field is known.
Electrons
Holes
Слайд 91

Magnetism Hall Geometry (+ Charge) Current is moving to the right.

Magnetism

Hall Geometry (+ Charge)

Current is moving to the right. (vd)
Magnetic field

will force the charge to the top.
This leaves a deficit (-) charge on the bottom.
This creates an electric field and a potential difference.
Слайд 92

Magnetism Negative Carriers Carrier is negative. Current still to the right.

Magnetism

Negative Carriers

Carrier is negative.
Current still to the right.
Force pushes negative charges

to the top.
Positive charge builds up on the bottom.
Sign of the potential difference is reversed.
Слайд 93

Magnetism Hall Math Eventually, the field due to the Hall effect

Magnetism

Hall Math

Eventually, the field due to the Hall effect will allow

the current to travel un-deflected through the conductor.
Слайд 94

Magnetic Fields Due to Currents Chapter 30

Magnetic Fields Due to Currents Chapter 30

Слайд 95

Magnetism Try to remember…

Magnetism

Try to remember…

Слайд 96

Magnetism For the Magnetic Field, current “elements” create the field. This,

Magnetism

For the Magnetic Field, current “elements” create the field.

This, defines B!

This is

the Law of
Biot-Savart
Слайд 97

Magnetism Magnetic Field of a Straight Wire We intimated via magnets

Magnetism

Magnetic Field of a Straight Wire

We intimated via magnets that the

Magnetic field associated with a straight wire seemed to vary with 1/d.
We can now PROVE this!
Слайд 98

Magnetism From the Past

Magnetism

From the Past

Слайд 99

Magnetism Right-hand rule: Grasp the element in your right hand with

Magnetism

Right-hand rule: Grasp the element in your right hand with your

extended thumb pointing in the direction of the current. Your fingers will then naturally curl around in the direction of the magnetic field lines due to that element.

Directions: The Right Hand Rule

Reminder !

Слайд 100

Magnetism Let’s Calculate the FIELD Note: For ALL current elements ds

Magnetism

Let’s Calculate the FIELD

Note:
For ALL current elements
ds X r
is into the

page
Слайд 101

Magnetism The Details

Magnetism

The Details

Слайд 102

Magnetism Moving right along Verify this. 1/d

Magnetism

Moving right along

Verify this.

1/d

Слайд 103

Magnetism A bit more complicated A finite wire

Magnetism

A bit more complicated A finite wire

Слайд 104

Magnetism P1

Magnetism

P1

Слайд 105

Magnetism More P1

Magnetism

More P1

Слайд 106

Magnetism P2

Magnetism

P2

Слайд 107

Magnetism APPLICATION: Find the magnetic field B at point P in

Magnetism

APPLICATION:
Find the magnetic field B at point P in for i

= 10 A and a = 8.0 cm.

A Combination of P2 geometries.

Слайд 108

Magnetism Circular Arc of Wire

Magnetism

Circular Arc of Wire

Слайд 109

Magnetism More arc…

Magnetism

More arc…

Слайд 110

Magnetism Howya Do Dat?? No Field at C

Magnetism

Howya Do Dat??

No Field at C

Слайд 111

Magnetism Force Between Two Current Carrying Straight Parallel Conductors Wire “a”

Magnetism

Force Between Two Current Carrying Straight Parallel Conductors

Wire “a” creates
a field

at wire “b”

Current in wire “b” sees a
force because it is moving
in the magnetic field of “a”.

Слайд 112

Magnetism The Calculation

Magnetism

The Calculation

Слайд 113

Magnetism Definition of the Ampere The force acting between currents in

Magnetism

Definition of the Ampere

The force acting between currents in parallel wires

is the basis for the definition of the ampere, which is one of the seven SI base units. The definition, adopted in 1946, is this: The ampere is that constant current which, if maintained in two straight, parallel conductors of infinite length, of negligible circular cross section, and placed 1 m apart in vacuum, would produce on each of these conductors a force of magnitude 2 x 10-7 newton per meter of length.
Слайд 114

TRANSITION AMPERE

TRANSITION

AMPERE

Слайд 115

Welcome to Andre’ Marie Ampere’s Law Normally written as a “circulation”

Welcome to Andre’ Marie Ampere’s Law

Normally written as a “circulation” vector

equation.
We will look at another form, but first…
Слайд 116

Magnetism Remember GAUSS’S LAW?? Surface Integral

Magnetism

Remember GAUSS’S LAW??

Surface
Integral

Слайд 117

Magnetism Gauss’s Law Made calculations easier than integration over a charge

Magnetism

Gauss’s Law

Made calculations easier than integration over a charge distribution.
Applied to

situations of HIGH SYMMETRY.
Gaussian SURFACE had to be defined which was consistent with the geometry.
AMPERE’S Law is the Gauss’ Law of Magnetism! (Sorry)
Слайд 118

Magnetism The next few slides have been lifted from Seb Oliver

Magnetism

The next few slides have been lifted from Seb Oliver on the

internet

Whoever he is!

Слайд 119

Magnetism Biot-Savart The “Coulombs Law of Magnetism”

Magnetism

Biot-Savart

The “Coulombs Law of Magnetism”

Слайд 120

Magnetism Invisible Summary Biot-Savart Law (Field produced by wires) Centre of

Magnetism

Invisible Summary

Biot-Savart Law
(Field produced by wires)
Centre of a wire loop

radius R
Centre of a tight Wire Coil with N turns
Distance a from long straight wire
Force between two wires
Definition of Ampere
Слайд 121

Magnetism Magnetic Field from a long wire I B r ds

Magnetism

Magnetic Field from a long wire

I

B

r

ds

Using Biot-Savart Law

Take a short vector

on a circle, ds

Thus the dot product of B & the short vector ds is:

Слайд 122

Magnetism Sum B.ds around a circular path I B r ds

Magnetism

Sum B.ds around a circular path

I

B

r

ds

Sum this around the whole ring

Circumference

of circle
Слайд 123

Magnetism Consider a different path Field goes as 1/r Path goes

Magnetism

Consider a different path

Field goes as 1/r
Path goes as r.
Integral independent

of r

i

Слайд 124

Magnetism SO, AMPERE’S LAW by SUPERPOSITION: We will do a LINE

Magnetism

SO, AMPERE’S LAW by SUPERPOSITION:

We will do a LINE INTEGRATION
Around a closed

path or LOOP.
Слайд 125

Magnetism Ampere’s Law USE THE RIGHT HAND RULE IN THESE CALCULATIONS

Magnetism

Ampere’s Law

USE THE RIGHT HAND RULE IN THESE CALCULATIONS

Слайд 126

Magnetism The Right Hand Rule

Magnetism

The Right Hand Rule

Слайд 127

Magnetism Another Right Hand Rule

Magnetism

Another Right Hand Rule

Слайд 128

Magnetism COMPARE Line Integral Surface Integral

Magnetism

COMPARE

Line Integral
Surface Integral

Слайд 129

Magnetism Simple Example

Magnetism

Simple Example

Слайд 130

Magnetism Field Around a Long Straight Wire

Magnetism

Field Around a Long Straight Wire

Слайд 131

Magnetism Field INSIDE a Wire Carrying UNIFORM Current

Magnetism

Field INSIDE a Wire Carrying UNIFORM Current

Слайд 132

Magnetism The Calculation Graph ????

Magnetism

The Calculation

Graph ????

Слайд 133

Magnetism

Magnetism

Слайд 134

Magnetism Procedure Apply Ampere’s law only to highly symmetrical situations. Superposition

Magnetism

Procedure

Apply Ampere’s law only to highly symmetrical situations.
Superposition works.
Two wires can

be treated separately and the results added (VECTORIALLY!)
The individual parts of the calculation can be handled (usually) without the use of vector calculations because of the symmetry.
THIS IS SORT OF LIKE GAUSS’s LAW WITH AN ATTITUDE!
Слайд 135

Magnetism The figure below shows a cross section of an infinite

Magnetism

The figure below shows a cross section of an infinite conducting

sheet carrying a current per unit x-length of l; the current emerges perpendicularly out of the page. (a) Use the Biot–Savart law and symmetry to show that for all points P above the sheet, and all points P´ below it, the magnetic field B is parallel to the sheet and directed as shown. (b) Use Ampere's law to find B at all points P and P´.
Слайд 136

Magnetism FIRST PART Vertical Components Cancel

Magnetism

FIRST PART

Vertical Components
Cancel

Слайд 137

Magnetism Apply Ampere to Circuit

Magnetism

Apply Ampere to Circuit

Слайд 138

Magnetism The “Math” Bds=0 Distance not a factor!

Magnetism

The “Math”

Bds=0

Distance not a factor!

Слайд 139

Magnetism A Physical Solenoid

Magnetism

A Physical Solenoid

Слайд 140

Magnetism Inside the Solenoid For an “INFINITE” (long) solenoid the previous

Magnetism

Inside the Solenoid

For an “INFINITE” (long) solenoid the previous problem and

SUPERPOSITION suggests that the field OUTSIDE this solenoid is ZERO!
Слайд 141

Magnetism More on Long Solenoid Field is ZERO! Field is ZERO Field looks UNIFORM

Magnetism

More on Long Solenoid

Field is ZERO!
Field is ZERO

Field looks UNIFORM

Слайд 142

Magnetism The real thing….. Weak Field Stronger - Leakage Fairly Uniform field Finite Length

Magnetism

The real thing…..

Weak Field

Stronger - Leakage

Fairly Uniform field

Finite Length

Слайд 143

Magnetism Another Way

Magnetism

Another Way

Слайд 144

Magnetism Application Creation of Uniform Magnetic Field Region Minimal field outside except at the ends!

Magnetism

Application

Creation of Uniform Magnetic Field Region
Minimal field outside
except at the ends!

Слайд 145

Magnetism Two Coils

Magnetism

Two Coils

Слайд 146

Magnetism “Real” Helmholtz Coils Used for experiments. Can be aligned to

Magnetism

“Real” Helmholtz Coils

Used for experiments.
Can be aligned to cancel
out the Earth’s

magnetic
field for critical measurements.
Слайд 147

Magnetism The Toroid Slightly less dense than inner portion

Magnetism

The Toroid

Slightly less
dense than
inner portion

- Предыдущая
Основные тригонометрические формулы
Следующая -
Wet Air - увлажнитель воздуха для людей болеющих астмой. Проект

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