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

Transcription

1 Magnetic materials, & inductance & Torque

2 Magnetic 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: a diamagnetic, da ag etc, paramagnetic, and ferromagnetic.

3 Magnetisation

4 Magnetisation

5 Magnetisation

6 Magnetic Properties of Matter or Magnetic materials Ferromagnetism - When a ferromagnetic material is placed near a magnet, it will be attracted toward the region of greater magnetic field. Iron, cobalt, nickel, gadolinium, dysprosium and alloys containing i these elements exhibit ferromagnetism because the electron spins within one atom interact with those of nearby atoms. Electron spins will align themselves, creating magnetic domains forming a permanent magnet. If a piece of iron is placed within a strong magnetic field, the domains in line with the field will grow in size as the domains perpendicular to the field will shrink in size.

7 Diamagnetism- When a diamagnetic material is placed near a magnet, it will be repelled from the region of greater magnetic field, just opposite to a ferromagnetic material. The orbital speed of the electrons is altered in such a way as to change the orbital dipole moment in a direction opposite to the external magnetic field. People and frogs are diamagnetic. Metals such as bismuth, copper, gold, silver and lead, as well as many nonmetals such as water and most organic compounds are diamagnetic.

8 Paramagnetism- When a paramagnetic material is placed near a magnet, it will be attracted to the region of greater magnetic field, like a ferromagnetic material. The difference is that the attraction ti is weak. The dipoles associated with the spins of unpaired electrons experience a torque tending to line them up parallel to the external field. It is exhibited by materials containing transition elements, rare earth elements and actinide elements. Liquidid oxygen and aluminum are examples of paramagnetic materials.

9 An idea about magnetic moments System Nucleus ~ Electron ~ Bar Magnet 5 Earth Magnetic dipole Moment (J/T)

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

11 Magnetic Dipole Moment

12 Magnetic Field in a Current Loop

13 Calculation of Bohr magneton Current tin the loop = Bohr s model i ia Orbital magnetic dipole moment q T qv 2r ev 2 evr r 2 r 2 mvr l nh 2 el 2mm

14 Bohr s magneton This is a basic unit of atomic magnetic dipole moment ia ev 2 r evr r 2 2 nh mvr 2 eh 24 B J / T 4 m

15 Sources of Magnetism We 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 properties of electrons, but it is helpful lto relate these properties back to the motion of charges. Every 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. 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.

16 Magnetic Properties of Materials Magnetization in a material is associated with atomic current loops generated by two principal mechanisms: Orbital motionsofof the electrons around the nucleus, i.e orbital magnetic moment, m o Electron spin about its own axis, i.e spin magnetic moment, m s

17 Spin Magnetic Dipole Moment Just 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 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 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 s, points up. Because of its spin, an electron is like a little bar magnet. μ s I N S

18 Orbital Magnetic Dipole Moment Imagine now a planet that not only rotates but also revolves around its star. If the planet had a net charge, its rotation would give it a spin magnetic dipole moment, and its revolution would give it an orbital magnetic dipole moment. Charge in motion once again produces a magnetic field. Since an electron s charge is negative, its orbit is like a current loop in the opposite direction. By the right hand rule, the angular momentum vector in the pic below would point down and the orbital magnetic dipole moment, μ orb, points up. An orbiting electron behaves like a tiny electromagnet with its N pole in the direction of μ orb. Remember, though, that in reality electrons are not like little planets. In quantum mechanics, instead of circular orbits we speak of electrons behaving like waves and we can only talk of their positions in terms of probabilities. μ orb I N S

19 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. The resultant vectors from each electron then combine for the whole atom, often canceling 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 atoms have all different orientations, the material as a whole remains nonmagnetic. Ferromagnetic materials, like iron, are comprised of atoms that each have net dipole moment. Furthermore, all the atoms have the same alignment, at least within very tiny regions called domains. The domains can have different orientations, ti though, h leaving the iron nonmagnetic except when placed in an external field. Permanent magnets are produced when the domains in a ferromagnetic material are aligned.

20 Permanent Magnets Each atom in a ferromagnetic material llike iron is like a little magnet, and these magnets are all aligned in tiny regions 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 Mid Atlantic Ridge beneath the Atlantic Ocean. Domains Lets melt the iron, and bring in a magnetic field. Now, when we let the solid cool down, and take away the external magnetic field, we have formed a permanent magnet in the same direction as external field. Temp Melting point Bar Magnet

21 Magnetic Permeability Magnetization vector M is defined as m M m H where = magnetic susceptibility (dimensionless) Magnetic permeability is defined as: 1 H/m where 0 m H m and relative permeability is defined as 1 r m 0

22 Relative Permeability

23 Relative permeability

24 Magnetic Materials Diamagnetic materials have negative susceptibilities. Paramagnetic materials have positive susceptibilities. However, the absolute susceptibilities value of both materials is in the order Thus, can be ignored. m r 1 or 0

25 Diamagnetism

26 Diamagnetism

27 Diamagnetism

28 Diamagnetism