M2 Magnetostatics 1

LECTURE 4 MAGNETOSTATICS INTRODUCTION AND APPLICATIONS (PART 1)

Outline 2

 Magnetism and magnets  History Hi t off Magnets M t  Types of Magnets  Magnetic field  Magnetic field line of forces  Magnet applications  Biot Savart’s law  Gauss’s law  Ampère’s law

1

Magnet song 3

Click on the image http://www.youtube.com/watch?v=G-nkIECIBWM

Magnetism 4

 A physical phenomenon produced by the motion of electric charge,

resulting in attractive and repulsive forces between objects.

http://www.youtube.com/watch?v=XiHVe8U5PhU

2

What are magnets? 5

mag·net ˈmagnət noun noun: magnet;

plural noun: magnets

a piece of iron (or an ore, alloy, or other material) that has its component atoms so ordered that the material exhibits properties of magnetism, such as attracting other iron-containing objects or aligning itself in an external magnetic field.

Iron

Nickel

http://periodictable.com/Samples/026.32/s13.JPG http://images-of-elements.com/cobalt.jpg

Cobalt

http://www.periodictable.com/Samples/028.17/s7s.JPG

Polarization 6 

Magnets are polarized. Every

magnet has a north and a south.

N



Magnetic north and south poles are always together.

N 

S

S

N

S

There are no magnetic monopoles.

3

History of Magnets 7

Click on the image

http://www.youtube.com/watch?v=u6v4J-CpKQE

Permanent Magnets 8

•

Once they have been magnetized they retain a certain degree of magnetism.

Magnetite

http://www.periodictable.com/Samples/060.2/s9s.JPG http://period8-2009.wikispaces.com/file/view/Magnetite.jpg/97048778/460x344/Magnetite.jpg

4

Shapes of Permanent Magnets 9

http://ed101.bu.edu/StudentDoc/Archives/ED101fa10/sjay0601/images/20060312083354!Bar_magnet.jpg http://www.thomasnet.com/articles/image/electrical-power-generation/nib-magnet.JPG http://www.heberger-image.fr/data/images/50198_aimant_different_modele.jpg

5

M2 Magnetostatics 1

LECTURE 4 MAGNETOSTATICS INTRODUCTION AND APPLICATIONS (PART 2)

Temporary magnets 2

• •

Magnets that simply act like permanent magnets when they are within a strong magnetic field. Unlike permanent magnets however, they loose their magnetism when the field disappears.

Paper clips

Iron nails https://epay.hawaii.edu:8443/C24372test_ustores/web/images/store_9/paper_clip_large.jpg http://www.commonnail.com/upfiles/common_nailswire_nailsiron_nails.jpg

1

Electromagnets 3

 Electromagnets are extremely strong magnets.  Magnetic fields are induced by current (motion of electric charges)  Electromagnets are widely used as components of other electrical

devices such as  

  

Electrical motors Maglev train

Headphones, stereo speakers, computer speakers Phone ringers Electron microscope, AFM, particle accelerator

I

http://upload.wikimedia.org/wikipedia/commons/4/41/Simple_electromagnet2.gif

Direct Current (DC) Motor 4

Magnet

Brush

Magnet Electromagnet

Simple DC motor circuit http://www.youtube.com/watch?v=Xi7o8cMPI0E

http://upload.wikimedia.org/wikipedia/commons/4/41/Simple_electromagnet2.gif http://www.learningaboutelectronics.com/images/DC-motor-circuit.png

2

Speakers and Microphones 5

See how speakers work!!!

http://www.techhive.com/article/2000201/three-minute-tech-speakers.html https://microphones.audiolinks.com/Microphones/micdiagram2922.jpg http://www.youtube.com/watch?v=LKuHuyaRiHg

Electromagnet Ringer 6

3

Scanning Electron Microscope 7

Magnetic lens

http://4.bp.blogspot.com/3FrRlleSObY/TVvFCdSiNI/AAAAAAAAAEM/BRBw3hk45vQ/s200/Scanning+Electron+Microscope.jpg http://nanolab.me.cmu.edu/projects/geckohair/images/CMU_NanoRobotics_Lab_Hierarchy_SEM.jpg http://www.purdue.edu/rem/rs/graphics/sem2.gif http://www.ammrf.org.au/myscope/images/tem/em-lens_function.png

ElectroMagnetic Suspension (EMS) Maglev Train 8

http://www.chinadiscovery.com/assets/images/shanghai/city-tour/shanghai-maglev-train.jpg http://www.hk-phy.org/articles/maglev/german_e.gif

4

Magnetic field 9

•

Magnetic field is the space surrounding a magnet, in which magnetic force is exerted.

attraction

repulsion http://www.schoolphysics.co.uk/age11-14/Electricity%20and%20magnetism/Magnetism/text/Magnetic_fields/index.html http://www.tutorvista.com/content/science/science-ii/magnetic-effects-electric-current/mapping-magnetic-lines.php http://upload.wikimedia.org/wikipedia/commons/1/14/Magnetic_field_of_bar_magnets_repelling.png

Magnetic field 10

•

If a bar magnet is placed in the magnetic field, it will experience magnetic forces. However, the field will continue to exist even if the magnet is removed.

S

N

http://www.superconductors.solidchem.net/sites/default/files/users/user1/MagnetSchoolFSU-Electromagnet.png

5

Magnetic Lines of Force 11

• •

A magnetic field is described by drawing the magnetic lines of force. A magnetic line of force is the path traced by a North magnetic pole free to move under the influence of a magnetic field.

6

M2 Magnetostatics 1

LECTURE 4 MAGNETOSTATICS INTRODUCTION AND APPLICATIONS (PART 3)

Properties of Magnetic Lines of Force 2

• •

• •

Lines of force are closed and continuous curves. Outside the magnet, the lines of force are directed from the north pole toward the south pole of the magnet, whereas within the magnet the magnetic lines are directed from the south pole towards the north pole. pole Lines of force repel each other. Lines of force never intersect.

http://www.youtube.com/watch?v=zbTrHWW3xvU

1

How is magnetic field created? 3

Oersted’s experiment Oersted Oersted’ss

experiment shows that current produces magnetic fields that loop around the conductor.

Click on the image http://www.youtube.com/watch?v=-w-1-4Xnjuw

How is a magnetic field created? 4

 Magnetic fields are produced by the motion of electrical charges.  Therefore, the current can produce the magnetic field.

http://demonstrations.wolfram.com/CreationOfAMagneticFieldByAnElectricCurrent/

2

Magnetic field intensity in other configurations 5 SOLENOID CLICK here! http://www.quantumdiaries.org/wp-content/uploads/2011/05/Solenoid.jpeg

TOROID CLICK here! http://www.wb5rvz.com/sdr/common/images/toroid_coil_22_turns.gif

Earth’s Magnetic Field 6

• The Earth's magnetic field is similar to that of a bar magnet tilted 11 degrees from the spin axis of the Earth. • The circulating electric currents in the Earth's molten metallic core are the origin of the magnetic field which gives a field similar to that of the earth. • The magnetic field magnitude measured at the surface of the Earth is about half a Gauss and dips toward the Earth in the northern hemisphere.

http://www.physics.sjsu.edu/becker/physics51/mag_field.htm http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magearth.html

3

Earth’s Magnetic Field 7

•

Earth’s magnetic field is a great shield to cosmic rays.

Click on the image http://www.youtube.com/watch?v=URN-XyZD2vQ

Can the Earth’s Magnetic Field Flip? 8

•

What happens if the earth’s magnetic field flips ?

4

Which type of field is present near a moving electric charge? 9

a) b) c) d)

Both an electric field and a magnetic field Neither an electric field nor a magnetic field An electric field only A magnetic field only

http://www.youtube.com/watch?v=uj0DFDfQajw

5

M2 Magnetostatics 1

LECTURE 4 MAGNETOSTATICS BIO SAVART’S LAW

Magnetic Field Intensity Calculation 2

H Vector quantity Unit: Ampere/m

1

Biot Savart’s Law 3

http://iesmonre.educa.aragon.es/alumnos0506/electricidad/biotsavart/biografia.htm

Biot Savart’s Law 4

Biot-Savart law states that “If a wire carries a steady current I, the magnetic field dH at some point P associated with an element of conductor length dl has the following properties: • The vector dH is perpendicular to both dl (the direction of the current I) and to the unit vector r directed from the element dl to the point P.”

2

Biot Savart’s Law 5

 H = magnetic field intensity (A/m) I = electric current (A)

 dl = line segment vector (m)  r = distance vector from a current line to point P (m) r = distance from a current line to point P (m)

dH

aˆ r = unit vector with the direction from a current line to point P

AP Physics C Montwood High School R. Casao

Mathematical Form of Biot Savart’s Law 6

Magnetic field from the current segment dl is

    Idl  a r Idl  r dH   4 r 2 4 r 3

A/m

The integration is required over the length l.

   Idl  r H  4 r 3

A/m

3

Recalling Coulomb’s law: Line of charge (1) Consider a charged wire, the test charge q0 is placed to measure the electric field at that position using Coulomb’s   law.  E E

En

2

+ q0

1

+ rn

r1 r2

 E

q1

+ + + q1 + q2

aˆ  2 1

4 0 r1

q2

+ + qn

aˆ  ...  2 2

4 0 r2

qn

4 r

2 0n

aˆ n  ...

For a continuous point charges, it is impossible to find the superpositioned electric field of a charged wire!

Recalling Coulomb’s law:  Line of charge (2)

Consider the electric field dE from each charge element dq along a charged wire of length l using  Coulomb’s law.  dq dE

dE 

+

+ q0

r

+ dq

l

4 0 r 2

aˆ r

 dq E aˆ 2 r 4 0 r l 

1

dqq aˆ r 4 0 l r 2

The problem can be solved using vector calculus.

4

Solving the Magnetic Field for Line of Current by Bio Savart’s Law (Coulomb’s Law Analogy) 9

z

Assumption: current elements are discrete. I

P r1

Using Superposition to Obtain the Total Magnetic Field. 10

z

Calculation of the magnetic field from each element I

r2

rn

……….

r1

P

    r1 Idl1  r1  Idl1  a dH 1   4 r12 4 r13  Idl 2  r 2 dH 2  4 r23    Idl n  r n dH n  4 rn 3

5

For Continuous Line of Current, It is Impossible to Find the Magnetic Field by Superposition. 11

The integration is required over the length l.

   Idl  r H  4 r 3

A/m

Step by Step: Magnetic Field in a Current-Conducting wire 12



z

Find Idl

 Idl  Idza Id ˆ z

I y



Find r

dl

r

 r  yaˆ y  zaˆ z

http://www.chem.ox.ac.uk/teaching/Physics%20for%20CHemists/Magnetism/Images/biot.jpg

6

Step by Step: Magnetic Field in a Current-Conducting wire 13

z

  Idl  r  Idzaˆ z  ( yaˆ y  zaˆ z )

I y

P

  Idl  r  Iydz (aˆ x )

dl

http://www.chem.ox.ac.uk/teaching/Physics%20for%20CHemists/Magnetism/Images/biot.jpg

Step by Step: Magnetic Field in a Current-Conducting wire 14

z

 3  2 2 3 r  r  (z  y )   3

I

dH1 x

P

dl

y

 (z2  y2 )3/2

   Idl  r Iydz (aˆ x ) dH 1   2 3 4 r ( z  y 2 )3/2

http://www.chem.ox.ac.uk/teaching/Physics%20for%20CHemists/Magnetism/Images/biot.jpg

7

Step by Step: Magnetic Field in a Current-Conducting wire 15

  H 1   dH 1

From



Iydz (aˆ x ) ( z 2  y 2 )3/2

  Iy 

dz (aˆ x ) 2 2 3/2 (z  y )

Step by Step: Magnetic Field in a Current-Conducting wire 16

Using the formula from Table of Integral

 yields

a

dx 2

x

2



3

 2



x

a  a  x2 2

2

 I (aˆ x ) H1  2 y



1 2

A/m /

8

If we calculate for H field at the same radial distance  from the current wire, we will obtain the same magnitude of the magnetic field as z

dH

dH

I

H dH

2

A/m

dH y

x



dH

I

dH

x

17

Right Hand Rule 18

The right hand rule can be used to determine the direction of the magnetic field around the current carrying conductor: Thumb of the right hand in the direction of the current. Fingers of the right hand curl around the wire in the direction of the magnetic field at that point.

H

http://scienceblogs.com/startswithabang/files/2009/04/Right_hand_rule.png

9

Magnetic Field in a Current-Conducting wire 19

CLICK

http://www.walter-fendt.de/ph14e/mfwire.htm

Summary of the Magnetic Field of the Conducting Wire 20

• The magnetic field lines are concentric circles that surround the wire in a plane perpendicular to the wire. • The magnitude of the magnetic field H is proportional to the current and decreases as the distance from the wire increases.

H

Watch this cool animation!

AP Physics C Montwood High School , R. Casao

10

1

 In our living world (macroscopic world), magnetism

arises from magnets (hard and soft magnetic materials), electromagnets, and current flow.

Flow of current in a coil causes magnetism

Magnet causes magnetism

2

 Technically speaking, we say that the source of

magnetism g is a magnetic g dipole p moment.

N

S

1

3

• At atomic and molecular levels (microscopic world), electrons : move in orbits around a nucleus similar to the earth moves in an orbit around the sun, : rotates (spin) around their own axes similar to the earth rotates around its own axis. • Movement of electrons in orbits and electron spin are equivalent q i l t to t charge h movementt and d is i the th source off magnetism or dipole moments. We can call them orbital dipole moment and spin dipole moment, respectively.

4

• In fact, the origin of all magnetism in magnetic materials are due to movement of electrons in orbits and electron spin. Magnetic dipole moment due to electron moving in orbit around nucleus

Magnetic dipole moment due to electron spinning around its own axis

• Net dipole moment of an atom is a vector sum of all orbital and spin dipole moments through their interaction. Imagine complexity of interactions of 26 orbital moments and 26 spin moment in one iron atom.

2

5

• When Fe atoms (and other magnetic atoms such as Ni Co) form solids, Ni, solids net moments of atoms further interact. This will cause net moments to point, to align, in the same direction within a small region called a magnetic domain. • Each domain will have a net dipole p moment, call magnetization, in one direction only. Sizes of magnetic domains are few tens of microns. • Different domains have different magnetization.

6

• A piece of magnetic materials (such as magnets) have millions off domains. d i L ft in Left i nature, t th they show no magnetism as net moments of different domains point in different directions. We can see domains with Kerr Microscopy technique.

3

7

• We can force moments in different domains to align in the same direction by applying external magnetic fields from permanent magnets or electromagnets. • Apply magnetic fields will exert force on moments in domains so that they are parallel applied field. Under such Condition, we say that materials - show net dipole moment, - exhibit magnetism, magnetism - become magnetized.

8

4