Unit IV_ Fundamentals of Magnetism and application
- 1. Fundamentals of Magnetism UNIT - IV 1
- 2. Objectives •The objective of this unit is to present the student the Fundamentals of Magnetism, student will have an understanding of •About Magnetism •The Bar Magnet •Guass’s law •Magnetic Force Objectives 2 •Magnetic Force •Magnetization and magnetic intensity •Solenoid and toroid •Magnetic Properties of materials •Permanent magnets, electromagnets •Earth’s magnetism
- 3. Introduction •Magnetism exists everywhere from tiny particles like electrons to the entire universe. Historically the word ‘magnetism’ was derived from iron ore magnetite (Fe3 O4 ). In olden days, magnets were used as magnetic compass for navigation 3 Magnetic fields due to a bar magnet and a circuital current.
- 4. Bar Magnet A bar magnet is a rectangular piece of an object, made up of iron, steel or any other ferromagnetic substance or ferromagnetic composite, that shows permanent magnetic properties. It has two poles, a north and a south pole such that when suspended freely, the magnet aligns itself so that the northern pole points towards the magnetic north pole of the earth. Types of Bar Magnet There are two types of bar magnets: Cylindrical bar magnet: A cylindrical rod is also known as a rod magnet that has 4 Cylindrical bar magnet: A cylindrical rod is also known as a rod magnet that has a thickness equal to larger than the diameter enabling high magnetism property. These bar magnets find application in educational, experimental, and research uses. Rectangular bar magnet: Rectangular bar magnets find applications in manufacturing and engineering industries as they have magnetic strength and field greater than the other magnets.
- 5. Bar Magnet Properties of Bar Magnet A bar magnet has properties similar to any permanent magnet. •It has a north pole and a south pole at two ends. Even if you break a bar magnet from the middle, both the pieces will still have a north pole and a south pole, no matter how many pieces you break it in. •Its magnetic force of it is the strongest at the poles. •If this magnet is suspended freely in the air with a thread, it will not come to rest until the poles are aligned in a north-south position. A Mariner’s Compass uses this property to determine direction. 5 Mariner’s Compass uses this property to determine direction. •If two bar magnets are placed close to each other, their unlike poles will attract and like poles will repel each other. •A bar magnet will attract all ferromagnetic materials such as iron, nickel and cobalt.
- 6. Bar Magnet Magnetic Field Lines around a Bar Magnet Let us understand the concept of magnetic field lines using the following activity. Let us sprinkle iron filings on a sheet of paper and a bar magnet in between. When we tap the paper, we notice that the fillings get aligned in the manner shown in the figure below. •The magnetic field lines can be defined as imaginary lines that can be drawn along the magnetic field that is acting around any magnetic substance. The magnetic field lines possess certain properties •The magnetic field lines of a magnet form continuous closed loops. 6 •The magnetic field lines of a magnet form continuous closed loops. •The tangent to the field line at any point represents the direction of the net magnetic field B at that point. •The larger the number of field lines crossing per unit area, the stronger the magnitude of the magnetic field B. •The magnetic field lines do not intersect.
- 7. Bar Magnet Uses of Bar Magnet •Bar magnets are used as stirrers in laboratories for magnetic experiments. •They also find applications in medical procedures. •Electronic devices such as telephones, radios, and television sets use magnets. •Many industries use bar magnets for the collection of loose metals and also for retaining the magnetism of other magnets. 7
- 8. Bar Magnet Repulsion or attraction between two magnetic dipoles •The force between two wires, each of which carries a current, can be understood from the interaction of one of the currents with the magnetic field produced by the other current. • For example, the force between two parallel wires carrying currents in the same direction is attractive. •It is repulsive if the currents are in opposite directions. •Two circular current loops, located one above the other and with their planes parallel, will attract if the currents are in the same directions and will repel if the currents are in opposite directions. •The situation is shown on the left side of Figure . When the loops are side by 8 side as on the right side of Figure , the situation is reversed. • For two currents flowing in the same direction, whether clockwise or counterclockwise, the force is repulsive, while for opposite directions, it is attractive. •The nature of the force for the loops depicted in Figure can be obtained by considering the direction of the currents in the parts of the loops that are closest to each other: same current direction, attraction; opposite current direction, repulsion.
- 9. Magnetism magnetism, phenomenon associated with magnetic fields, which arise from the motion of electric charges. This motion can take many forms. It can be an electric current in a conductor or charged particles moving through space, or it can be the motion of an electron in an atomic orbital. Magnetism is also associated with elementary particles, such as the electron, that have a property called spin. 9
- 10. Gauss’s Law Gauss’s law for magnetism states that the magnetic flux B across any closed surface is zero; that is, div B = 0, where div is the divergence operator. This law is consistent with the observation that isolated magnetic poles (monopoles) do not exist. 10
- 11. Magnetic forces Magnetic forces Lorentz force A magnetic field B imparts a force on moving charged particles. The entire electromagnetic force on a charged particle with charge q and velocity v is called the Lorentz force (after the Dutch physicist Hendrik A. Lorentz) and is given by 11 The first term is contributed by the electric field. The second term is the magnetic force and has a direction perpendicular to both the velocity v and the magnetic field B. The magnetic force is proportional to q and to the magnitude of v × B. In terms of the angle ϕ between v and B, the magnitude of the force equals qvB sin ϕ. An interesting result of the Lorentz force is the motion of a charged particle in a uniform magnetic field. If v is perpendicular to B (i.e., with the angle ϕ between v and B of 90°), the particle will follow a circular trajectory with a radius of r = mv/qB.
- 12. Magnetic forces Magnetic forces Lorentz force •If the angle ϕ is less than 90°, the particle orbit will be a helix with an axis parallel to the field lines. •If ϕ is zero, there will be no magnetic force on the particle, which will continue to move undeflected along the field lines. •Charged particle accelerators like cyclotrons use the fact that particles move in a circular orbit when v and B are at right angles. 12 •For each revolution, a carefully timed electric field gives the particles additional kinetic energy, which makes them travel in increasingly larger orbits. When the particles have acquired the desired energy, they are extracted and used in a number of different ways, from fundamental studies of the properties of matter to the medical treatment of cancer.
- 13. Magnetization Magnetization •Regardless of the direction of the magnetic field in Figure , a sample of copper is magnetically attracted toward the low field region to the right in the drawing. This behaviour is termed diamagnetism. •A sample of aluminum, however, is attracted toward the high field region in an effect called paramagnetism. •A magnetic dipole moment is induced when matter is subjected to an external field. For copper, the induced dipole moment is opposite to the direction of the external field; for aluminum, it is aligned with that field. •The magnetization M of a small volume of matter is the sum (a vector sum) of the magnetic dipole moments in the small volume divided by that volume. •M is measured in units of amperes per metre. 13 •M is measured in units of amperes per metre. •The degree of induced magnetization is given by the magnetic susceptibility of the material χm, which is commonly defined by the equation
- 14. Magnetization Magnetization The field H is called the magnetic intensity and, like M, is measured in units of amperes per metre. (It is sometimes also called the magnetic field, but the symbol H is unambiguous.) The definition of H is The effect of ferromagnetic materials in increasing the magnetic field produced by current loops is quite large 14 by current loops is quite large
- 15. Magnetic Intensity Magnetic Intensity The net magnetic moment per unit volume of the material is known as intensity of magnetisation. It is a vector quantity 15 - The SI unit of intensity of magnetisation is ampere metre-1
- 16. Toroid Toroid •Figure illustrates a toroidal winding of conducting wire around a ring of iron that has a small gap. The magnetic field inside a toroidal winding similar to the one illustrated in Figure 10 but without the iron ring is given by B = μ0Ni/2πr, where r is the distance from the axis of the toroid, N is the number of turns, and i is the current in the wire. •If the same toroid is wound around an iron ring with no gap, the magnetic field inside the iron is larger by a factor equal to μ/μ0, where μ is the magnetic permeability of the iron. 16 •If the gap is 1 cm wide, the field in that gap is about 0.12 tesla, a 60-fold increase relative to the 0.002-tesla field in the toroid when no iron is used. •This factor is typically given by the ratio of the circumference of the toroid to the gap in the ferromagnetic material. The maximum value of B as the gap becomes very small.
- 17. Magnetic properties Magnetic properties a) Magnetising field The magnetic field which is used to magnetize a sample or specimen is called the magnetising field. Magnetising field is a vector quantity b) Magnetic permeability The magnetic permeability is the measure of ability of the material to allow the passage of magnetic field lines through it or measure of the capacity of the substance to take magnetisation or the degree of penetration of magnetic field through the substance. 17 In free space, the permeability (or absolute permeability) is denoted by µ0 and for any other medium it is denoted by µ.The relative permeability µr is defined as the ratio between absolute permeability of the medium to the permeability of free space. Relative permeability is a dimensionless number and has no units. For free space (air or vacuum), the relative permeability is unity i.e., µr = 1.
- 18. Magnetic properties of Materials Magnetic properties of Materials •All matter exhibits magnetic properties when placed in an external magnetic field. Even substances like copper and aluminum that are not normally thought of as having magnetic properties are affected by the presence of a magnetic field such as that produced by either pole of a bar magnet. Depending on whether there is an attraction or repulsion by the pole of a magnet, matter is classified as being either paramagnetic or diamagnetic, respectively. A few materials, notably iron, show a very large attraction toward the pole of a permanent bar magnet; materials of this kind are called ferromagnetic. •In 1845 Faraday became the first to classify substances as either 18 •In 1845 Faraday became the first to classify substances as either diamagnetic or paramagnetic. He based this classification on his observation of the force exerted on substances in an inhomogeneous magnetic field. At moderate field strengths, the magnetization M of a substance is linearly proportional to the strength of the applied field H. The magnetization is specified by the magnetic susceptibility χ (previously labeled χm), defined by the relation M = χH •.
- 19. Magnetic properties of Materials Magnetic properties of Materials •If the magnetic susceptibility χ is positive, the force is in the direction of increasing field strength, whereas if χ is negative, it is in the direction of decreasing field strength. Measurement of the force F in a known field H with a known gradient dH/dx is the basis of a number of accurate methods of determining χ. •Substances for which the magnetic susceptibility is negative (e.g., copper and silver) are classified as diamagnetic. The susceptibility is small, on the order of −10−5 for solids and liquids and −10−8 for gases. 19 order of −10 for solids and liquids and −10 for gases. •A characteristic feature of diamagnetism is that the magnetic moment per unit mass in a given field is virtually constant for a given substance over a very wide range of temperatures. It changes little between solid, liquid, and gas; the variation in the susceptibility between solid or liquid and gas is almost entirely due to the change in the number of molecules per unit volume. This indicates that the magnetic moment induced in each molecule by a given field is primarily a property characteristic of the molecule.
- 20. Magnetic properties of Materials Magnetic properties of Materials •Substances for which the magnetic susceptibility is positive are classed as paramagnetic. In a few cases (including most metals), the susceptibility is independent of temperature, but in most compounds it is strongly temperature dependent, increasing as the temperature is lowered. Diamagnetism When an electron moving in an atomic orbit is in a magnetic field B, the force exerted on the electron produces a small change in the orbital motion; the electron orbit precesses about the direction of B. As a result, each 20 motion; the electron orbit precesses about the direction of B. As a result, each electron acquires an additional angular momentum that contributes to the magnetization of the sample •Paramagnetism occurs primarily in substances in which some or all of the individual atoms, ions, or molecules possess a permanent magnetic dipole moment. The magnetization of such matter depends on the ratio of the magnetic energy of the individual dipoles to the thermal energy. This dependence can be calculated in quantum theory and is given by the Brillouin function, which depends only on the ratio (B/T). At low magnetic fields, the magnetization is linearly proportional to the field and reaches its maximum saturation value when the magnetic energy is much greater than the thermal energy.
- 21. Magnetic properties of Materials Magnetic properties of Materials •Figure 15 shows the dependence of the magnetic moment per ion in units of Bohr magnetons as a function of B/T. (One Bohr magneton equals 9.274009994 × 10−24 ampere times square metre.) 21
- 22. Magnetic properties of Materials Magnetic properties of Materials 22
- 23. Earth’s Magnetism Earth’s Magnetism •The earth’s magnetic field lines mimic a (hypothetical) magnetic dipole positioned at its centre. The dipole’s axis does not correspond with the earth’s axis of rotation, but it is now titled by approximately 11.3 degrees concerning the latter. The magnetic poles, in this view, are the points at which the dipole’s magnetic field lines enter or depart the earth. •The magnetic South pole of the Earth is located at the geographical North pole, while the magnetic North pole is located at the geographical South pole. The earth’s magnetic South pole tends to attract the compass’s North pole, which is 23 why the compass’s magnet faces north. Theories of Earth’s Magnetism There are multiple theories regarding Earth’s magnetism. However, two are more prominent: •The dynamo theory •The ionisation theory
- 24. Earth’s Magnetism Earth’s Magnetism •Dynamo Theory of Earth’s Magnetism •The dynamo theory describes how a celestial entity, such as the Earth or a star, generates and maintains a magnetic field over long time scales (millions of years). Key points describing the earth’s magnetism are: •Convection in the outer core, together with the Coriolis effect (caused by the earth’s rotation), produces a self-sustaining (geodynamo) magnetic field, according to dynamo theory. •The Earth’s magnetic field is formed in the planet’s outer core. The metal in the outer core is fluid because the outer core has a lower pressure than the inner core. The temperature of the outer core varies between 4400 and 6000 degrees Celsius near the inner core. 24 near the inner core. •Variations in temperature, pressure and composition inside the outer core generate convection currents in the molten iron, as the cool, dense matter sinks and heated, less dense matter rises •The movement of liquid iron generates electric currents, which eventually form magnetic fields •Charged metals passing across these fields generate electric currents, which keep the cycle going. Geodynamo is the name given to this self-sustaining cycle. •Independent magnetic fields are virtually aligned in the same direction due to the spiral movement of charged particles caused by the Coriolis force, culminating in the planet’s single massive magnetic field.
- 25. Earth’s Magnetism Earth’s Magnetism Declination On Earth, magnetic and geographical north do not correspond. Magnetic declination is the angle formed by magnetic North and geographical North. Geographic North is never fixed in the horizontal plane; it shifts with the location of the Earth’s surface and magnetic declination follows . Thus, the angle between magnetic north (the direction the northern end of a compass needle points) and true north is known as magnetic declination. When magnetic north is east of true north, the declination is positive. 25 Inclination The angle formed by a compass needle held vertically is known as magnetic inclination. At the place of measurement, positive inclination values imply that the field is pointing downward into the Earth. Thus, the magnetic inclination is the angle formed by a horizontal plane on the Earth’s surface. It’s also called the dip angle. The angle of dip is 0 degrees at the magnetic equator and 90 degrees at the magnetic poles.
- 26. Earth’s Magnetism Earth’s Magnetism Ionization of the Outer Layer Earth revolves both on its axis and around the Sun, as we all know. As the Earth’s outer layer gets ionized, this spinning generates an electric current. Because these ions are moving, they produce magnetic field. However, the Dynamo effect is a more plausible explanation because this magnetic field is so faint. Meaning of True north True north is the direction along the earth’s surface that leads to the true North Pole, also known as the geographical North Pole. It’s also known as geodetic 26 north and it’s distinct from magnetic north, the direction shown by a compass and grid north, which is the direction indicated by grid lines pointing north. Meaning of Magnetic North The north direction, shown by a compass needle, runs parallel to the earth’s magnetic field.