Magnetic materials, inductancefolk.uio.no › ravi › cutn › elec_mag › 11_mag_dipole-torque.pdf · • This is a basic unit of atomic magnetic dipole moment ev evr 2 2 r2 r

Magnetic materials, & inductance & Torque g , q

P.Ravindran, PHY041: Electricity & Magnetism 8 February 2013: Magnetic materials, inductance, and torque

Magnetic Properties of MaterialsMagnetic Properties of Materials

Magnetic behavior of a material is due to the interaction of magnetic dipole moments of its atoms with an external magnetic field.

This behavior is used as a basis for classifying magnetic materials.

3 types of magnetic materials: diamagnetic, 3 ypes o ag e c a e a s d a ag et c,paramagnetic, and ferromagnetic.


Magnetisation


Magnetisation


Magnetisation


Magnetic Properties of Matteror Magnetic materialsor Magnetic materials

Ferromagnetism - When a ferromagnetic material is placed nearg g pa magnet, it will be attracted toward the region of greatermagnetic field. Iron, cobalt, nickel, gadolinium, dysprosium andll t i i th l t hibit f ti balloys containing these elements exhibit ferromagnetism because

the electron spins within one atom interact with those of nearbyatomsatoms.

Electron spins will align themselves, creating magnetic domainsforming a permanent magnet. If a piece of iron is placed withina strong magnetic field, the domains in line with the field will

i i th d i di l t th fi ld ill h i kgrow in size as the domains perpendicular to the field will shrinkin size.


Diamagnetism- When a diamagnetic material is placed near amagnet, it will be repelled from the region of greater magneticfield, just opposite to a ferromagnetic material.

The orbital speed of the electrons is altered in such a way as tochange the orbital dipole moment in a direction opposite to thechange the orbital dipole moment in a direction opposite to theexternal magnetic field.

People and frogs are diamagnetic. Metals such as bismuth,copper, gold, silver and lead, as well as many nonmetals such as

ater and most organic compo nds are diamagneticwater and most organic compounds are diamagnetic.


Paramagnetism- When a paramagnetic material is placed near amagnet, it will be attracted to the region of greater magneticfield, like a ferromagnetic material. The difference is that thett ti i kattraction is weak.

The dipoles associated with the spins of unpaired electronsThe dipoles associated with the spins of unpaired electronsexperience a torque tending to line them up parallel to theexternal field.

It is exhibited by materials containing transition elements, rareearth elements and actinide elements Liq id o gen andearth elements and actinide elements. Liquid oxygen andaluminum are examples of paramagnetic materials.


An idea about magnetic momentsg

System Magnetic dipoleSystem Magnetic dipole Moment (J/T)

N l 10 28Nucleus ~ 10-28

El t 10 23Electron ~ 10-23

B M t 5Bar Magnet 5

Earth 1022Earth 1022


Atomic and nuclear magnetism Magnetic properties depend upon magnetic properties of the

individual atoms.

Magnetic material is consists of atomic dipoles where dipole moment associated with circulation of electron.

We consider magnetic materials to be composed of a collection of atomic dipoles.

These dipoles might align when an external electric field is applied.

l i l i b h l b id d An electron circulating about the nucleus can be considered as a current loop of radius r and speed v.


Magnetic Dipole Moment


Magnetic Field in a Current Loop


Calculation of Bohr magneton

C t i th l qvqi• Current in the loop = r

qvTqi

2

222 evrr

reviA

• Bohr’s model

22 rnhmvrBohr s model2

mvr

• Orbital magnetic dipole momentm

ell 2


m2

Bohr’s magnetonBohr s magneton

• This is a basic unit of atomic magnetic dipole• This is a basic unit of atomic magnetic dipole moment

evrev22

2 evrrr

eviA

nhmvr 2

mvr

eh TJm

ehB /1027.9

424


Sources of MagnetismWe have seen charges in motion (as in a current) produce magnetic fields. This is one source of magnetism.

Another source is the electron itself. Electrons behave as if they were tiny magnets. Quantum mechanics is required to explain fully the magnetic

i f l b i i h l f l l h i b k hproperties of electrons, but it is helpful to relate these properties back to the motion of charges.

Every electron in an atom behaves as a magnet in two ways each having twoEvery electron in an atom behaves as a magnet in two ways, each having two magnetic dipole moments:

Spin magnetic dipole moment ‐ due to the “rotation” of an electron.Spin magnetic dipole moment due to the rotation of an electron.

Orbital magnetic dipole moment ‐ due to the “revolution” of an electron about the nucleus.

Note: Electrons are not actually little balls that rotate and revolve like planets, but imagining them this way is useful when explaining magnetism without quantum mechanics


quantum mechanics.

Magnetic Properties of Materials• Magnetization in a material is associated with atomic current loops generated by two principalcurrent loops generated by two principal mechanisms:– Orbital motions of the electrons around the nucleus, i.eOrbital motions of the electrons around the nucleus, i.eorbital magnetic moment, mo

– Electron spin about its own axis, i.e spin magnetic p , p gmoment, ms


Just as electrons have the intrinsic properties of mass and charge, they have an intrinsic

Spin Magnetic Dipole MomentJust as electrons have the intrinsic properties of mass and charge, they have an intrinsic property called spin. This means that electrons, by their very nature, possess these three attributes. You’re already comfortable with the notions of charge and mass. To understand spin it will be helpful to think of an electron as a rotating sphere or planet. However, this is p p g p p ,no more than a helpful visual tool.

Imagine an electron as a soccer ball smeared with negative charge rotating about an axis. By the right hand rule the angular momentum of the ball due to its rotation points downBy the right hand rule, the angular momentum of the ball due to its rotation points down. But since its charge is negative, the spinning ball is like a little current loop flowing in the direction opposite its rotation, and the ball becomes an electromagnet with the N pole up. For an electron we would say its spin magnetic dipole moment vector μ points upFor an electron we would say its spin magnetic dipole moment vector, μs, points up. Because of its spin, an electron is like a little bar magnet.

Nμs

‐‐

‐ ‐‐ ‐‐

IS


‐ ‐

Orbital Magnetic Dipole MomentImagine now a planet that not only rotates but also revolves around its star. If the planetImagine now a planet that not only rotates but also revolves around its star. If the planethad a net charge, its rotation would give it a spin magnetic dipole moment, and itsrevolution would give it an orbital magnetic dipole moment. Charge in motion once againproduces a magnetic field.p g

Since an electron’s charge is negative, its orbit is like a current loop in the oppositedirection. By the right hand rule, the angular momentum vector in the pic below wouldpoint down and the orbital magnetic dipole moment μ points up An orbiting electronpoint down and the orbital magnetic dipole moment, μorb, points up. An orbiting electronbehaves like a tiny electromagnet with its N pole in the direction of μorb. Remember,though, that in reality electrons are not like little planets. In quantum mechanics, instead ofcircular orbits we speak of electrons behaving like waves and we can only talk of theircircular orbits we speak of electrons behaving like waves and we can only talk of theirpositions in terms of probabilities.

μorbN

S‐ I

S


Materials and Magnetism Each electron in an atom has two magnetic dipole moments associated with it, one

for spin, and one for orbit. Each is a vector.

These two dipole moments combine vectorially for each electron.p y

The resultant vectors from each electron then combine for the whole atom, oftencanceling each other out.

For most materials the net dipole moment for each atom is about zero.

For some materials each atom has a nonzero dipole moment, but because the atomshave all different orientations, the material as a whole remains nonmagnetic.

Ferromagnetic materials, like iron, are comprised of atoms that each have net dipolemoment. Furthermore, all the atoms have the same alignment, at least within veryti i ll d d i Th d i h diff t i t ti th htiny regions called domains. The domains can have different orientations, though,leaving the iron nonmagnetic except when placed in an external field.

Permanent magnets are produced when the domains in a ferromagnetic material are


aligned.

Permanent Magnets

E h t i f ti t i l likEach atom in a ferromagnetic material like iron is like a little magnet, and these magnets are all aligned in tiny regions called domains At high temps these

Lets melt the iron, and bring in a magnetic field.

h l h lid

Temp

called domains. At high temps these domains can align in the presence of an external field (like Earth’s) leaving a permanent magnet This happens at the

Now, when we let the solid cool down, and take away the external magnetic field, we h f d t

Melting point

permanent magnet. This happens at the Mid‐Atlantic Ridge beneath the Atlantic Ocean.

have formed a permanent magnet in the same direction as external field.

Domains


Bar Magnet

Magnetic Permeability

• Magnetization vector M is defined asHM m

where = magnetic susceptibility (dimensionless)

• Magnetic permeability is defined as:m

• Magnetic permeability is defined as:

H/m 10 m mH104 where 70

and relative permeability is defined as

0 m 0

mr 1

0


0

Relative Permeability


Relative permeability


Magnetic Materials

• Diamagnetic materials have negative susceptibilities.• Paramagnetic materials have positive susceptibilities.• However, the absolute susceptibilities value of both materials is in the order 10‐5. Thus, can be ignored.materials is in the order 10 . Thus, can be ignored. m

or1 0or 1 r


Diamagnetism


Diamagnetism


Diamagnetism


Diamagnetism


Documents

Magnetic materials, inductancefolk.uio.no › ravi › cutn › elec_mag › 11_mag_dipole-torque.pdf · • This is a basic unit of atomic magnetic dipole moment ev evr 2 2 r2 r