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ELEC 3105 Basic EM and Power Engineering Lecture Topics Sources of magnetic fields Magnetization M B, H, and M relationship Diamagnetic materials Paramagnetic materials Ferromagnetic materials Magnetostatics POSTULATE 2 FOR THE MAGNETIC FIELD A current element I d produces a magnetic field B which at a distance R is given by: From postulate 2: Currents in wires produce magnetic fields. o I Rˆ dB d 4 R 2 dB Units of {T,G,Wb/m2} 2 26 3 4 Qm is considered as an equivalent magnetic charge. Magnetic charges do not exist but some times it is easier to think that they do in order to visualize cause and effect in magnetic field situations. Qm would be for the entire 5 bar magnet. qm is considered as an equivalent magnetic charge that produces the same magnetic field as a current loop of current I. qm would be for a single current loop. Note that the loop can be formed by a single spinning electron about the nucleus. 6 Equivalent views of the bar magnet The magnetization M of the bar can be interpreted through the two points of view. The tiny magnets produced by electrons spinning about the nucleus are the source of the magnetic field produced by a bar magnet and magnetizable materials. This can be formalized by introducing the magnetization. (Describes the MAGNET in the macroscopic domain) 8 The magnetization M is defined as the average dipole moment per unit volume: m M v The units of {M} are Amperes per meter. v A m is a small volume that contains many atomic dipoles. Knowing M implies that we not concern ourselves with the individual atomic dipole moments. Recall p P v for polarization Equivalent charge formulism sm Magnetic surface charge density Equivalent current formulism K Magnetic surface current density m 11 B H M o o B H M 12 Mag. Flux density. Mag. Field strength Magnetization H B H M o o o This term gives the contribution to the flux density B due to the real current I in the windings of the toroid. M o This term gives the additional contribution to the flux density B due to the induced magnetization M in the core material. 13 For an air core toroid we have: M 0 Thus B H M o o becomes B H o When M 0 we can rewrite B o H o M 1 in a similar linear relationship 2 FROM 1 2 we can obtain: B H M 1 H o 14 M 1 Thus H Introducing the relative permeability: o M 1 H r Magnetostatics Then Permeability r o r Permeability of free space Relative permeability for a medium o H m o 4 107 15 Exact constant Permeability of the medium H Wb m m 4 We will now examine the nature of the magnetization M The three classes of magnetic materials are: DIAMAGNETIC PARAMAGNETIC FERROMAGNETIC The material is characterized by the effect they have on the magnetic field. In the case chosen we will examine the magnetic field of a solenoid. Of course you have materials which16are non-magnetic o P When no magnetic material is introduced in the solenoid the magnetic field at the point P is Bo. Introducing various cores in the solenoid we observe that Bo changes to B DIAMAGNETIC B 1 B o PARAMAGNETIC B 1 B o FERROMAGNETIC 17 B 1 B o 18 * Diamagnetic materials M 1H r Linear function Diamagnetic materials display no permanent magnetization. That is, when H is removed M vanishes. M H m m 0. 19 * Diamagnetic materials WHY? • Results from the orbital motion of the electrons • Each circulating electron acts as a current loop producing a magnetic field • Two electrons travel in each orbit and in opposite direction • The magnetic moment produced my each electron of the orbit cancel. • This explains why diamagnetic materials have no residual magnetization. What happens when a magnetic field is applied. • One electron in the orbit will speed up • One electron in the orbit will slow down. • Effect is such that net magnetic moment is opposite to the applied field. 20 Diamagnetic materials WHY? • Results from the orbital motion of the electrons • Each circulating electron acts as a current loop producing a magnetic field • Two electrons travel in each orbit and in opposite direction • The magnetic moment produced my each electron of the orbit cancel. • This explains why diamagnetic materials have no residual magnetization. What happens when a magnetic field is applied. • One electron in the orbit will speed up • One electron in the orbit will slow down. • Effect is such that net magnetic moment is opposite to the applied field. There is a reduction in the magnetic flux density. B 1 B Bo applied B measured in material o 21 Diamagnetic materials A diamagnetic material placed in a magnetic field is repelled, pushed out of the magnetic field region. The effect is very small. FI since F is greatest where B is greatest. 2 m I B I Diamagnetic materials 23 Diamagnetism Push me a grape. A grape is repelled by both the north and south poles of a strong rare-earth magnet. The grape is repelled because it contains water, which is diamagnetic. Diamagnetic materials are repelled by magnetic poles. Material • Two large grapes • Drinking straw • Film canister with lid • Push pin • Small knife or razor blade • Neodymium magnet Assembly Insert the push pin through the underside of the film canister lid and put the lid on the canister so that the point of the pin is sticking out. Find the center of the drinking straw and use the knife to cut a small hole, approximately 0.5 cm x 1 cm. (You can also use the hot tip of a soldering gun to melt a hole.) Push one grape onto each end of the straw. Balance the straw with the grapes on the point of the push pin; the point of the pin goes through the small hole on the straw. 24 Paramagnetic materials M 1H r Linear function Paramagnetic materials display no permanent magnetization. That is, when H is removed M vanishes. M H m m 0. 27 Paramagnetic materials WHY? • Results from the spin motion of the electron • Each electron has an magnetic moment • Thermal motion randomly orients the associated magnetic moments • This explains why paramagnetic materials have no residual magnetization. What happens when a magnetic field is applied. • The axis of the spins for the electrons align in the direction of the field • Magnetic dipoles tend to align with the magnetic field • Alignment is only partial due to thermal effects. B o 28 Paramagnetic materials N S Aluminum A paramagnetic material placed in a magnetic field is attracted into the higher magnetic field regions. The effect is very small. FI since F is greatest where B is greatest. 29 2 m I B I Paramagnetic materials M 1H r M H m Linear function Temperature dependence of M mB kT M Nmcoth( ) kT mB Temperature dependence of m Nm 3kT 2 o m 30 m 0. Ferromagnetic materials M H 1H r H H r Are functions of the applied magnetic field H. m Ferromagnetic region M H H m Tc = Currie temperature Paramagnetic region Ferromagnetic materials WHY? • Results from the spin motion of the electron • Strong inter molecular fields are present which act on individual electron spins • Spins of the molecules align over small regions called domains • No external field is required to align spins within a domain • No net magnetization observed since domain moments point in random directions. What happens when a magnetic field is applied. 32 Ferromagnetic materials WHY? What happens when a magnetic field is applied. • As the magnetic filed is increased, the domain which is most closely aligned with the applied magnetic field will grow. This growth is at the expense of those domains not in alignment with the applied magnetic field. • Domain growth continues until the entire material consist of one domain. • Domain rotation will then occur in order to complete the alignment of the magnetic moment with the applied filed, saturating the effect. Ferromagnetic materials show hysteresis in the B versus H curve. 33 Ferromagnetic materials WHY? What happens when we cycle the applied magnetic field. Ferromagnetic materials SOFT and HARD Ferromagnetic materials Area of hysteresis loop is equivalent to energy lost in one cycle. (Proof Soft ::: transformer cores, solenoids, …. Hard :: permanent magnets found in transformer loss mechanisms) Ferromagnetic materials 36 Ferromagnetic materials 37 Ferromagnetic materials no domains remain Behaves as a paramagnetic material 38 Ferromagnetic materials A ferromagnetic material placed in a magnetic field is strongly attracted towards the regions of higher magnetic field. FI since F is greatest where B is greatest. m constant B I Curie Point When a piece of iron gets too hot, it is no longer attracted to a magnet. A piece of iron will ordinarily be attracted to a magnet, but when you heat the iron to a high enough temperature (called the Curie point), it loses its ability to be magnetized. Heat energy scrambles the iron atoms so that they can't line up and create a magnetic field. Here is a simple demonstration of this effect Material A small magnet. (Radio Shack's disk magnets work fine.) A stand to hold the magnet pendulum and wire. (The stand can be easily made from Tinkertoys™ or pieces of wood.) One 6-volt lantern battery (or other 6-volt power supply). 2 electrical lead wires with alligator clips at both ends (available at Radio Shack). One 3-inch (8 cm) length of thin iron wire, obtainable by separating one strand from braided picture-hanging wire. String, about 1 foot (30 cm) long. 40 Note Radio Shack is now “The Source” Curie Point Assembly (15 minutes or less) To do and notice Make a stand from Tinkertoys™ or other wood as shown in the diagrams. Suspend the magnet from the top of the stand with a string. Make a pendulum at least 4 inches (10 cm) long. Stretch the iron wire between two posts so that, at its closest, the wire is 1 inch (2.5 cm) from the magnet. (15 minutes or more) Touch the magnet to the iron wire. It should magnetically attract and stick to the wire. Connect the clip leads to the terminals of the lantern battery. Connect one clip lead to one side of the iron wire, and touch the other clip lead to the iron wire on the opposite side of the magnet. Current will flow through the iron wire, causing the wire to heat up. (CAUTION: The wire will get hot!) As the iron heats up and begins to glow, the magnet will fall away from the wire. Take a clip lead away from the iron wire. Let the iron wire cool. When the iron wire is cool, notice that the magnet will stick to it once again. If the wire does not heat up enough to glow red, move the clip leads closer together. 41 Curie Point What’s going on: The iron wire is made of atoms that act like tiny magnets, each one having a north and south pole of its own. These iron atoms usually point in all different directions, so the iron has no net magnetic field. But when you hold a magnet up to the iron, the magnet makes the iron atoms line up. These lined-up atomic magnets turn the iron into a magnet. The iron is then attracted to the original magnet. High temperatures can disturb this process of magnetization. Thermal energy makes the iron atoms jiggle back and forth, disturbing their magnetic alignment. When the vibration of the atoms becomes too great, the atomic magnets do not line up as well, and the iron loses its magnetism. The temperature at which this occurs is called the Curie point Inside the earth, there is a core of molten iron. This iron is at a temperature above the Curie point and therefore can't be magnetized. Yet the earth is magnetized, with a north and a south magnetic pole. The magnetic field of the earth comes from an electromagnet, that is, from electrical currents flowing inside the liquid metal core. 42