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Angular Momentum of the Atom Electric Current and so the proto11kinetic energy is Magnetic Field . Solvi~~gfor the speed v, gives The radius needed to accoln~nodate5 -MeV protots is give11by Structure 11.1 Introduction Objec'tives 11.2 Response of Various Substance to a Magnetic Field 11.3 Magnetic Moment and Angular Momellturn of an Atom 11.4 Diamagnetism and Paramagnetism Diagmagnetism -Effect of Magnetic Field on Atomic Orbits Paramagnetism -Torque on Magnetic Dipoles 11.5 The Interaction of an Atom with Magnetic Field - Larmor Precession 11.6 Magnetisation of Paramagnets 11.7 Suminary 11.8 Tenninal Questions 11.9 Solutioils and Answers 11.1 INTRODUCTION In the last two Units, we have discussed the magnetic fields produced by moving , charges or cuirents in conductors. There, the moving charges and conductors were considered to be placed in vacuum (i.e., in air). In Units 11 and 12, we learn how the magnetic field affects materials and how some materials produce magnetic field. You lnust have learnt in your school Physics Course that in equipinei~tsuch as generator and motor, iron or iron alloy is used in their structure for the purpose of enhancing the magnetic flux and for confining it to a desired region. Therefore, we will study the magnetic properties of iron and a few other materials called ferromagnets, which have similar properties as iron. We sliall also learn that all the materials are affected by the magnetic field to some extent, though the effect in some cases is weak. When wespeak of magnetism in everyday conversation, we almost certaiiily have in mind an image of a bar magnet. You may have observed that a magnet can be used to lift nails, tacks, safety pins, and needles (Fig. 1l.la) while, on the other hand, you cannot use a magnet to pick up a piece of wood or paper (Fig. 1l.lb). TACKS MADE OP w MAGrnC BLOCK OP MATERIAL WOOD Fi~11.1:a) Materials that are athdalto a magnet are uUedmagnctic mabdds b) Mabrlrls Lbal do not read to 8 magnet arc called nonmagnetic mabhls. Materials such as mils, needles etc., which are i~lfluellcedby a magnet are called magnetic materials whereas other materials, like wood or paper, are called non-magnetic materials, However, this does not mean that there is no effect of magnetic field on non-magnetic materials. The difference between the behaviour of . , such materials and iron like magnetic materials is that the effect of magnetic field on non-magnetic material is very weak. There are two types of non-magnetic materials: diamagnetic and paramagnetic. Unit 11 deals with diamagnetic and paramagnetic effects. The ideas, concepts and various tenns Electric Current and that you become familiar with in this Unit would help you in the study of Mnguelic Field fenornagnetism in the next Unit. In this unit, we present a simple classical account of the magnetism, based on notion of classical physics. But you must keep in mind that it is not possible to understand the magnetic effects of materials from the point of view of classical physics. The magnetic effectsare a completely quantum mechanical phenomena. Only modem quantum physics is capable of giving a detailed explanation of the magnetic properties of matter because the study requires the introduction and utilization of quantum mechanical properties of atom. For a co~n~leteexplanation, one must take recourse to quantum mechanics; however, a lot, though i~icomnplete,of information about matter call be extracted by combining classical and quantum concepts. Basically, in this unit, we will try to understand, in a general way, the atomic origin of the various magnetic effects. The next unit is an extension of this unit. There, we wiIl try to develop a treatment of nlagnetised matter based on some observed relations between the magnetic field and the parameters whichcharacterise the material. Finally, we consider the analysis of the magnetic circuit, which is of particular importance in the design of the electromagnets. Objectives After studying this unit you should be able to: r understand and explain: gyromagnetic ratio, paramagnetism, diamagnetism, Larmor frequency, e reIate the magnetic dipole moment of an atomic magnet with its angular inomeiitum, c expIain the phenomena of diamagnetism in terms of Faraday inductio~land Lelu's principle, o explain panmagnetism in terms of the torque on magnetic dipoles, e find the precessional frequency of an atomic dipole in a magnetic field, o appreciate that a lot of information about magnetism of matter can be obtained from the classical ideas of ato~nicmagnetism. 11.2 RESPONSE OF VARIOUS SUBSTANCE TO A GNETIC FIELD To show how the magnetic materials respond to a magnetic field, consider a strong electromagnet, which has one sharply pointed pole piece and one flat pole piece as shown in Fig. 11.2. Small piece of malerial Fig.ll.21 A mall cylinder of bismuth is weakly repelled bithe sharp pde; a piece of aluminium is attracted. The magnetic field is much stronger in the region near the pointed pole whereas near the flat pole the field is weaker. This is because the lines must concentrate on the pointed pole. When the current is passed through the electromagnet (i.e., when the magnet is turned on), the hanging material is slightly displaced due to the small force 66 acting on it. Some materials get displaced in the direction of increasing field, i.e., towards the pointed pole. Such materials are paralnagiletic materials. Examples of such material are aluminium and liquid oxygen. On the other hand, there are materials like . bismuth, which are attracted in the direction qf the decreasing field, i.e., it gets repelled from the pointed pole. Such materials are called diamag~letic.Finally, there is a small class of materials which feel a considerable stronger force ( 10 - 10 times ) towards the pointed pole. Such substances are called ferromagnetic materials. Examples are iron and magnetite. HOW does a substance experience a force in a magnetic field? And why does the force act in a particular direction for some substance while in opposite direction for other substance? If we can answer these questions, we will understand the mechanisms of pramagnetism, diamagnetism and ferromagnetism. In Unit 9, you have already leanit that the magnetic fields are due to electric charges in motion. In fact, if you could examine a piece of'material on an atomic scale, you would visualize tiny current loops due to (i) electrons orbiting around nuclei and (ii) electrons spinning on their axes. For, macroscopic purposes, these current loops are so small that they are regarded as the magnetic dipoles (see Section 9.2 of Unit 9) having magnetic moment. It is this magnetic moment, via which the atom at a substance iiiteract with the external field, and give rise to diamagnetic and paramagiletic effects. In this unit, you will understand the origin of paramagnetism and diamagnetism. Fernmagnetism has been left to be explained in the next unit. Let us first find out the value of the magnetic moment and see how it is related to the angular momentum of the atom. 11.3 GNETIC MOMENT AND ANGULAR ILTOMEN'IVM OF AN ATOM Study comment: You may find it useful to look back at Unit 9, Section 9.2.2, in which the idea of magnetic dipoles has been introduced. Electrons in an atom are in coilstant motion arouild the nucleus. To describe their motion, one needs quantum mechailics, however, in this unit we shall use only classical arguments to obtain our results, though we repeat here that our description of the physical world is incomplete as we shall be leaving out quantum mechanics. We consider an electron in the atom to be moving, for simplicity, in a circular orbit around the nucleus under the influence of a central force, known as the electrostatic force, as show11 in Fig. 11.3(a). As a result of this motion, the electron will have an angular momentum L about the nucleus. Fbll.31 n) Cldcal model of an atom in wbich an eltclron moves nl speed v in n drrular orbit. b) The average elcchic cumnl is the same ns if the charge - e were divided iato small bils, fonning a rotating ring d charge. c) The orbital angular momentum vector and the magnetic mommt vector both point ia opposite dindona The magnitude of this angular momentum is given by the product of the mass m of the electron, its speed v and the radius r of the circular path (see Fig. 11.3), i.e., L = mvr Its direction is perpendicular to the plane of the orbit. As you have already read Unit 9, and worked out the terminal questions given at the end of that unit, the fact that orbital - Elcclric Cumtand motion of the electron constitutes an electric current will immediately strike your mind. Magnetic Field The average electric current is the same as if charge on electron were distributed in small bits, forming a rotating ring of charge, as shown in Fig. 11.3@). The magnitude of this current is the charge times the frequency as this would equal to the charge per unit time passing through any point on its orbit. The frequency of rotati011 is the reciprocal of the period of rotation &/v, hence the frequency of rotation has the value v/%. The current is then The magnetic moment due to this current is the product of the current and the area of which the electron path is the boundary, that is, p = I JW.2. Hence we have evr p = -- 2 It is also directed perpendicular to the plane of the orbit.
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