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PHYS2012 mag03.doc MAGNETISM AND MATERIALS All matter is composed of atoms and atoms are composed of protons, neutrons and electrons. The protons and neutrons are located in the atom's nucleus and the electrons are in “constant motion” around the nucleus. Electrons carry a negative electrical charge and produce a magnetic field as they move through space. A magnetic field is produced whenever an electrical charge is in motion. This may be hard to visualize on a subatomic scale but consider an electric current flowing through a conductor. When the electrons (electric current) are flowing through the conductor, a magnetic field forms around the conductor. The magnetic field can be detected using a compass. Since all matter is comprised of atoms, all materials are affected in some way by a magnetic field. However, not all materials react the same way. At the atomic level, the motion of an electron gives rise to current loop magnetic dipole moment magnetic field (like a miniature bar magnet) Magnetic dipole moment m pm mu u [A.m2] pm N i A n direction – right hand screw rule Magnetization M [A.m-1] magnetic dipole moment per unit volume M magnetic moment volume The magnetic moments associated with atoms have three origins: 1 The electron orbital motion. 2 The change in orbital motion caused by an external magnetic field. 3 The spin of the electrons. 4 Nuclear spins (will ignore in this course) When a material is placed within a magnetic field, the material's electrons will be affected. However, materials can react quite differently to the presence of an external magnetic field. This reaction is dependent on a number of factors such as the atomic and molecular structure of the material, and the net magnetic field associated with the atoms. mag03.doc June 28, 2017 1 In most atoms, electrons occur in pairs. Each electron in a pair spins in the opposite direction, so when electrons are paired together, their opposite spins cause there magnetic fields to cancel each other. Therefore, no net magnetic field exists. Alternately, materials with some unpaired electrons will have a net magnetic field and will react more to an external field. Most materials can be classified as ferromagnetic, diamagnetic or paramagnetic. B, H and M fields B o ( H M ) M m H B o (1 m ) H o r H H r 1 m o (1 m ) M m H only has meaning if one can define the relative permeability of the material. The relationship is valid for diamagnetic and paramagnetic materials but may not be valid for ferromagnetic materials. DIAMAGNETIC MATERIALS m 0 m 105 r 1 Small and negative susceptibility. Slightly repelled by a magnetic field. Do not retain the magnetic properties when the external field is removed. Magnetic moment – opposite direction to applied magnetic field. Solids with all electrons in pairs - no permanent magnetic moment per atom. Properties arise from the alignment of the electron orbits under the influence of an external magnetic field. Most elements in the periodic table, including copper, silver, and gold, are diamagnetic. m temperature independent provided no structural changes in material. m(argon) ~ -1.010-8 m(copper) ~ -1.010-5 B Diamagnetic material m < 0 (small) B = o (1+ m ) H H mag03.doc Permeability = o (1+ m ) =slope of B-H line June 28, 2017 2 PARAMAGNETIC MATERIALS m 0 small Small and positive susceptibility. Slightly attracted by a magnetic field. Material does not retain the magnetic properties when the external field is removed. Properties are due to the presence of some unpaired electrons and from the alignment of the electron orbits caused by the external magnetic field. Examples - magnesium, molybdenum, lithium, and tantalum. m(oxygen) ~ 2.010-6 m(aluminum) ~ 2.110-5 B Ideal magnetic material or paramagnetic material m > 0 (small) B = o r H = H = constant = slope of B-H curve H FERROMAGNETIC MATERIALS Large and positive susceptibility. Strong attraction to magnetic fields. Retain their magnetic properties after the external field has been removed. Some unpaired electrons so their atoms have a net magnetic moment. Strong magnetic properties due to the presence of magnetic domains. In these domains, large numbers of atomic moments (1012 to 1015) are aligned parallel so that the magnetic force within the domain is strong. When a ferromagnetic material is in the un-magnetized state, the domains are nearly randomly organized and the net magnetic field for the part as a whole is zero. When a magnetizing force is applied, the domains become aligned to produce a strong magnetic field within the part. Iron, nickel, and cobalt are examples of ferromagnetic materials. B o ( H M ) Magnetization is not proportional to the applied field. m(ferrite) ~ 100 m(iron) ~ 1000 mag03.doc June 28, 2017 3 Magnetic Domains Ferromagnetic materials get their magnetic properties not only because their atoms carry a magnetic moment but also because the material is made up of small regions known as magnetic domains. In each domain, all of the atomic dipoles are coupled together in a preferential direction. This alignment develops as the material develops its crystalline structure during solidification from the molten state. Magnetic domains can be detected using Magnetic Force Microscopy (MFM) and images of the domains like the one shown below can be constructed. Magnetic Force Microscopy (MFM) image showing the magnetic domains in a piece of heat treated carbon steel. During solidification a trillion or more atomic dipole moments are aligned parallel so that the magnetic force within the domain is strong in one direction. Ferromagnetic materials are said to be characterized by "spontaneous magnetization" since they obtain saturation magnetization in each of the domains without an external magnetic field being applied. Even though the domains are magnetically saturated, the bulk material may not show any signs of magnetism because the domains develop themselves are randomly oriented relative to each other. Ferromagnetic materials become magnetized when the magnetic domains within the material are aligned. This can be done my placing the material in a strong external magnetic field or by passing an electrical current through the material. Some or all of the domains can become aligned. The more domains that are aligned, the stronger the magnetic field in the material. When all of the domains are aligned, the material is said to be magnetically saturated. When a material is magnetically saturated, no additional amount of external magnetization force will cause an increase in its internal level of magnetization. Unmagnetized Material mag03.doc Magnetized Material June 28, 2017 4 Domain walls move and domains grow in the alignment of the atomic magnetic dipoles. The mobility of the domain walls is reduced by impurities and lattice imperfections. The coercivity (how easy for a magnetic material to be de-magnetized) is determined by the mobility of the domain walls. M 0 M 0 H external magnetic field mag03.doc June 28, 2017 5 THE HYSTERESIS LOOP AND MAGNETIC PROPERTIES A great deal of information can be learned about the magnetic properties of a material by studying its hysteresis loop. A hysteresis loop shows the relationship between the induced B-field (magnetic flux density) B and the H-field (magnetizing force) H. It is often referred to as the B-H loop. An example hysteresis loop is shown below. [Note: B does not become saturated only M does] The loop is generated by measuring the B-field of a ferromagnetic material while the Hfield is changed. A ferromagnetic material that has never been previously magnetized or has been thoroughly demagnetized will follow the dashed line as H is increased. As the line demonstrates, the greater the amount of current applied (H+), the stronger the B-field (B+). At point "a" almost all of the magnetic domains are aligned and an additional increase in the magnetizing force will produce very little increase in the B-field. The material has reached the point of magnetic saturation. When H is reduced back down to zero, the curve will move from point "a" to point "b." At this point, it can be seen that some B-field remains in the material even though the magnetizing force is zero. This is referred to as the point of retentivity on the graph and indicates the remanence or level of residual magnetism in the material. Some of the magnetic domains remain aligned but many have lost there alignment. As the magnetizing force is reversed, the curve moves to point "c", where the B-field has been reduced to zero. This is called the point of coercivity on the curve. The reversed H-field force has flipped enough of the domains so that the net B-field within the material is zero. The H-field required to remove the residual magnetism from the material, is called the coercive force or coercivity of the material. mag03.doc June 28, 2017 6 As the H-field is increased in the negative direction, the material will again become magnetically saturated but in the opposite direction (point "d"). Reducing H to zero brings the curve to point "e." It will have a level of residual magnetism equal to that achieved in the other direction. Increasing H back in the positive direction will return B to zero. Notice that the curve did not return to the origin of the graph because some Hfield is required to remove the residual magnetism. The curve will take a different path from point "f" back the saturation point where it with complete the loop. Permeability Permeability is a property that describes the ease with which a B-field is established in a material. It is the ratio of the B-field to the H-field B H It is clear that this equation describes the slope of the curve at any point on the hysteresis loop. The permeability value given in papers and reference materials is usually the maximum permeability or the maximum relative permeability. The maximum permeability is the point where the slope of the B/H curve for unmagnetized material is the greatest. This point is often taken as the point where a straight line from the origin is tangent to the B/H curve. The relative permeability r is arrived at by taking the ratio of the material's permeability to the permeability in free space (air) o. r = / mag03.doc June 28, 2017 7 Magnetization or B-H Curve http://www.electronics-tutorials.ws/electromagnetism/magnetic-hysteresis.html For a ferromagnetic material, the relative permeability is not a constant, r >> 1. mag03.doc June 28, 2017 8 MAGNETIZATION – macroscopic view Consider a long solenoid with no magnetic core of length L and crosssectional area A and N turns. From Ampere’s Circulation Law B-field (magnetic induction) B0 0 n I 0 H-fielod (magnetic intensity) H 0 n I 0 Now put a magnetic material inside the solenoid - it becomes magnetized. Atomic magnetic dipoles in the material line up, producing an internal magnetic field, which may strengthen (or oppose – diamagnetic material only) the original field. Magnetic field in the material can be seen as the result of effective currents of the atoms' magnetic dipoles. Magnetization M = total magnetic dipole moment per unit volume. Internal currents cancel, results in bound surface current For a paramagnetic or ferromagnetic material the B-field increases B(total) = B(current in coil) + B(material) B = B0 + Bm im mag03.doc June 28, 2017 9 B 0 n I 0 0 n im N im L N im A 0 H 0 L A N pm 0 H 0 Vol 0 H 0 M H n I0 0 H 0 B 0 H M M m H magnetic dipole moment pm im A Vol L A magnetization M dipole moment/volume N pm Vol B o (1 m ) H o r H H r 1 m o (1 m ) As the current (and hence applied field H) increases, magnetization M and magnetic field B increases. If H is small or substance weakly magnetic (paramagnetic), increase is linear. measure from graph r B/H o If H is large or substance strongly magnetic (e.g. ferromagnetic), as H increases, the magnetization M (and hence B) may increase nonlinearly - high field region where slope decreases is called "saturation" region max M. measure from graph r B/H o Since r varies with H could also use “differential permeability” dB/dH The shape of the hysteresis loop tells a great deal about the material being magnetized. The hysteresis curves of two different materials are shown in the graphs below. “hard” magnetic materials: Hc (coercivity) is high, area of the loop is large, used for permanent magnets. “soft” magnetic materials: Hc is small, area of loop is small, used for transformer cores & electromagnets. N.B. mag03.doc very difference scales for the H-field June 28, 2017 10 soft r large hard r Material can be demagnetized by striking or heating it, or go round the hysteresis loop, gradually reducing its size. "Degaussing" Energy dissipation – hysteresis loop W is the energy dissipated within a unit volume of the sample (increase in internal energy of the sample) in the process in taking the sample around the hysteresis loop. Transformers must be made of materials that have narrow hysteresis loops. mag03.doc June 28, 2017 11 Consider taking the sample through one cycle of the hysteresis loop. Since there is a changing magnetic flux, an emf is generated as the current in the coil changes. induced emf N current i power P = i dm dB NA dt dt HL N W P dt cycle energy dissipated W i dt cycle A L H dB Vol cycle dB H L NA dt dt N cycle H dB cycle So, the work/volume is equal to the area enclosed by the hysteresis loop. permanent magnets T < Tc carbon steel alnico V platinum-cobalt Nd2Fe (sintered) high permeability materials iron 4% Si-Fe Mu metal Supermalloy M282 mag03.doc Remanence magnetism Br (T) 1 1.25 0.45 1 Coercivity HC (A.m-1) 4103 4104 2105 2106 r (max) Saturation Bsat (T) Coercivity HC (A.m-1) 5103 7103 1105 8105 2.1 2.0 0.65 0.8 80 40 4 0.16 M587 June 28, 2017 12 PERMANENT MAGNETS Bar Magnets There are no free currents - the magnet is magnetized all by itself if = 0 H dl 0 H-field inside and the H-field outside point in opposite directions B dA 0 the magnetic field lines for B must be continuous, the lines just keep going on (there are no magnetic monopoles). Inside the magnet: H 1 BM o lines of H point in a direction opposite to M and B . Outside the magnet: M 0 B and H have the same field pattern HH B mag03.doc June 28, 2017 13 6 S 2 1 4 N HFe 1 H 5 2 0 Hair 2 3 Circulation loop: square side L 3 5 6 2 4 5 dl HFe dl Hair dl Hair dl 1 Bair H air 6 3 5 5 2 4 HFe dl 0 H Fe dl H Fe dl Hair dl Hair dl H Fe H air Gauss’s Law f or magnetism Cylindrical Gaussian surface Binside Aoutside Ainside Boutside B dA Binside A Boutside A 0 Binside Boutside B-f ield lines – f orm continuous loops B M M 0 H N pole im Bound surf ace currents i m (right hand screw rule) mag03.doc M B June 28, 2017 14 Interaction between magnetic fields Like poles repel Unlike poles attract Magnetic Field of Like and Unlike Poles Together mag03.doc June 28, 2017 15 Why does a magnet stick to a piece of iron? un-magnetized piece of iron Bar magnet bought near un-magnetized piece of iron B N N N Bar magnet will attract the iron that was initially un-magnetized north pole attracts south pole Consider a magnetic field B to be non-uniform in which the B field points in a direction orthogonal to the plane of the current loop. There is a net force that pulls the magnetic dipole pm towards the region of high magnetic field. Proof The forces all pull the current elements outwards. The force on each current element is F = BiL Forces F3 and F4 cancel. F1 > F2 since the B-field is non uniform, the B-field larger on the left than the right. So there is a net force that pulls the magnetic dipole towards the region of larger magnetic field. B B large B small m F4 F1 F2 F3 i Explain what happens in the following diagrams when a magnet is placed on a ramp. Fe ramp mag03.doc Cu ramp June 28, 2017 plastic ramp 16 Uniformly magnetized sphere B-field H-field B-field continuous loops (no beginning or end) The H-field lines start where the M lines end and finish where M start. H-field has de-magnetizing effect since H and M are in opposite direction. M245 mag03.doc M301 June 28, 2017 17 Horse Shoe Magnets A permanent iron magnet is in the form of circular disk with a radius, r and a small gap in it of width, a. For the case when r >> a, discuss the H-field, B-field and magnetization for this example of a horse shoe magnet. Circulation loop f or circulation integration used in applying Ampere’s Law N Use Amperes’s Law for a loop around the permanent magnetic (i = 0) H dl if H iron (2 r a ) H air (a) 0 The H-field in the iron, Hiron must point in the opposite direction to the H-field in the air, Hair. Ampere’s Law B dA 0 The B-field field is perpendicular to the plane surfaces of the ring, and the perpendicular component of the B field is constant at an interface, so B is constant throughout the ring, B = Bair = Biron In the air gap H air B o or B = o Hair N In the iron H iron a a H air B 2 r a (2 r a ) o The H-field inside the magnet is in the opposite direction to the magnetization and has a demagnetizing effect. Hair Hiron This corresponds to a points on the hysteresis loop H > 0 & B < 0 or H < 0 and B > 0. For soft materials, the de-magnetizing effect is usually sufficient to bring the material back to B = 0 (M = 0) i.e., an un-magnetized state. This is why a horse-shoe magnet is stored with an iron keeper. Then, the B-field, H-field and magnetization all point in the same direction. mag03.doc June 28, 2017 18 M014 M169 M014 M169 mag03.doc M245 M282 M314 June 28, 2017 M587 19