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# Summarized Notes - 12th-JEE-Physics-Magnetism

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A physical phenomenon produced by the motion of electric charge, which results in attractive and repulsive forces between objects.

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### Summarized Notes - 12th-JEE-Physics-Magnetism

1. 1. 9011041155 / 9011031155 ∙ Live Webinars (online lectures) with recordings. ∙ Online Query Solving ∙ Online MCQ tests with detailed solutions ∙ Online Notes and Solved Exercises ∙ Career Counseling 1
2. 2. 9011041155 / 9011031155 Magnetism Circular Current loop as a magnetic dipole B= m Ia2 0 2 (a + x 2 …….(1) 2 3/2 ) For x >>> a, we may neglect the term a2. We have Ia2 0 2x 3 B ……..(2) But the area of the loop A = πa2 A a2 B .…….(3) IA 2 x3 ………(4) 0 M = IA 0 M 2 x3 Hence, B B 0 4 …….(5) 2M x3 …….(6) 2
3. 3. 9011041155 / 9011031155 Electric field of a dipole is E 2P 4 0 x ……….(7) 3 From equations (6) and (7), μ0 is analogous to 1 0 Magnetic dipole moment M is analogous to electrostatic dipole moment P and magnetic field is analogous to electrostatic field. A planar current loop is equivalent to a magnetic dipole of dipole moment M = IA which is analogous to electric dipole moment P. Thus we have shown that a current loop produces a magnetic field and behaves like a magnetic dipole. It     M B when experiences a torque given by, placed in external magnetic field and also it generates its own magnetic field. 3
4. 4. 9011041155 / 9011031155 Magnetic dipole moment of a revolving electron Period of revolution 2 r v T ……(8) Circulating current I I e 2 r v circumfernece velocity e T …….(9) ev 2 r …….(10) Magnitude of magnetic moment associated with circular current is 4
5. 5. 9011041155 / 9011031155 M0 M0 IA ev 2 r …..(11) r2 evr 2 …….(12) The direction of this magnetic moment is into the plane of paper. Negatively charged electron is moving in anticlockwise direction, leading to a clockwise current. Multiplying and dividing the right hand side of equation (12) by the mass of electron, me then M0 e me Vr 2me …….(13) 5
6. 6. 9011041155 / 9011031155 M0 e 2me ……..(14) L0 Here L0 = me Vr = angular momentum of the electron revolving round the nucleus.   e  ……(15) In vector, M0 L0 2me The negative sign indicates that the orbital angular momentum of electron is opposite in the direction to the orbital magnetic moment. The ratio of magnetic dipole moment with angular momentum of revolving electron is called the gyromagnetic ratio. Gyromagnetic ratio M0 L0 e 2me constant 1010 C / kg = 8.8 The circular orbit of electrons produce an orbital magnetic moment. In addition to the orbital magnetic 6
7. 7. 9011041155 / 9011031155 moment, the electron has an intrinsic magnetic moment called the spin magnetic moment. 7
8. 8. 9011041155 / 9011031155 Magnetization and magnetic intensity The net magnetic dipole moment per unit volume is  called as the magnetization MZ of the sample. Magnetization  MZ Net magnetic moment Volume Mnet Volume Magnetization is the vector quantity having unit A/ m and dimensions [L-1 M0 T0 I1]. magnetization of a paramagnetic sample is directly proportional to the external magnetic field and inversely proportional to the absolute temperature. i.e. MZ MZ Bext and MZ 1 T Bext T 8
9. 9. 9011041155 / 9011031155 MZ C Bext T …….(18) Equation (18) is known as Curie‟s Law and C is called Curie constant. 9
10. 10. 9011041155 / 9011031155 The magnetization of a ferromagnetic material such as iron can be studied with an arrangement called Toroid with an iron core as shown in fig. The material is formed into a thin toroidal core of circular crossection. A toroidal coil having n turns per unit length is wrapped around the core and carries current I. The coil is long solenoid bent into a circle. If iron core were not present, the magnitude of the magnetic field inside the coil would be B0 = μ0nI …….(19) Where μ0 is the permeability of vacuum 10
11. 11. 9011041155 / 9011031155 However, if iron core were present, the magnetic field    B inside the coil is greater than B0 . We can write magnitude of this field as …….(20) B = B0 + BM Where BM is the magnetic field contributed by the iron core. It turns out that this additional field BM is directly proportional to the magnetization MZ of the iron. BM = μ0 MZ ……(21) Magnetic intensity is a quantity used in describing magnetic phenomenon in terms of their magnetic fields. 11
12. 12. 9011041155 / 9011031155 The strength of magnetic field at a point can be given in terms of vector quantity called as magnetic intensity (H). Magnetic intensity „B0‟ is given by the relation, B0 = μ0H …….(22) where H = nI has the same dimensions and unit as MZ. Magnetic intensity has unit A / m and dimensions [L-1 M0 T0 I1]. Total magnetic field B is written as B = μ0 (H + MZ) Magnetization …..…(23) and magnetic mathematically expressed as, 12 intensity is
13. 13. 9011041155 / 9011031155 …….(24) MZ = XH where X is called the magnetic susceptibility. Magnetic susceptibility is small and positive for paramagnetic materials. Magnetic susceptibility is small and negative for diamagnetic materials. From equations (23) and (24) we obtain B = μ0 (1 + X) H ………(25) ∴ B = μ0 μr H ………(26) ∴ B = μH ………(27) where μr = 1 + X, is a dimensionless quantity called the relative magnetic permeability of the substance. μ = μ0 μr = μ0 (1 + X) ……..(28) 13
14. 14. 9011041155 / 9011031155 Diamagnetic Substances The substances which are weakly repelled by the magnetic field are called diamagnetic substances. Origin 1. For diamagnetic substances, the dipole moments of electrons in an atom cancel each other. Hence, the resultant magnetic moment of an atom is zero. 2. When an external magnetic field is applied, the induced magnetic moments oppose the applied magnetic field. Therefore, the diamagnetic substances are repelled by the magnet. 14
15. 15. 9011041155 / 9011031155 Properties 1. If a rod made-up of diamagnetic substance is placed in a non uniform magnetic field, it moves from stronger part of the field to the weaker part of the field. 2. If a rod made-up of a diamagnetic substance is placed in a uniform magnetic field, it comes to rest with its length perpendicular to the direction of the magnetic field. 3. When a solution of a diamagnetic substance is taken in a watch glass and is kept between two dissimilar poles of the magnets, there is a small depression at the middle. 4. When a diamagnetic liquid is taken in a U shaped glass tube and one of its arms is held in between two dissimilar poles of the magnets, liquid level in that arm is lowered. 15
16. 16. 9011041155 / 9011031155 5. When a diamagnetic gas is passed through two poles of the magnets, it spreads at right angles to the direction of the magnetic field. Examples : Antimony, gold, bismuth, mercury, water, air, hydrogen are diamagnetic in nature. Paramagnetic Substances The substances which are weakly attracted by the magnetic field are called paramagnetic substances. Origin 1. For paramagnetic substances, the dipole moments of electrons in an atom do not cancel each other. Hence, each atom has a resultant magnetic moment. 2. Each atom in a paramagnetic substance acts as a small magnetic dipole, called “ atomic magnet” 16
17. 17. 9011041155 / 9011031155 3. In the absence of magnetic field, atomic magnets are randomly oriented; hence, paramagnetic substances have zero resultant magnetic moment. 4. When an external magnetic field is applied, the atomic magnets are oriented so that their moments are in the direction of the magnetic field. Hence, the paramagnetic substances are magnetized in the external field. 5. When the external magnetic field is removed, the alignment of the atomic magnets is disturbed and the paramagnetic substances magnetism. 17 loose their
18. 18. 9011041155 / 9011031155 Properties 1. If a rod made-up of paramagnetic substance is placed in a non uniform magnetic field, it moves from weaker part of the field to the stronger part of the field. 2. If a rod made-up of a paramagnetic substance is placed in a uniform magnetic field, it comes to rest with its length parallel to the direction of the magnetic field. 3. When a solution of a paramagnetic substance is taken in a watch glass and is kept between two dissimilar poles of the magnets, there is a small elevation at the middle. 4. When a paramagnetic liquid is taken in a U shaped glass tube and one of its arms is held in between two dissimilar poles of the magnets, liquid level in that arm is raised. 18
19. 19. 9011041155 / 9011031155 5. When a paramagnetic gas is passed through two poles of the magnets, it spreads in the direction of the magnetic field. Examples : Aluminium, manganese, platinum, chromium, oxygen are paramagnetic in nature. 19
20. 20. 9011041155 / 9011031155 Ferromagnetic Substances The substances which are strongly attracted by a magnet are called ferromagnetic substances. The properties of ferromagnetic substances are similar to that of the paramagnetic substances, but they are large in extent. When the external field is removed these substances do not loose their magnetism completely. Origin The origin of ferromagnetism can be explained on the basis of domain theory. 20
21. 21. 9011041155 / 9011031155 Magnetic Domains A small region in which the magnetic moments of all the atomic magnets are lined in the same direction is called a domain. Each domain has a certain magnetic moment. 1. According to the domain theory, a. a ferromagnetic substance is made-up of number of small regions called domain. b. all the atomic magnets have the same direction of dipole moment, so that the domain has some resultant magnetic moment. 2. In the absence of external magnetic field, the domains are randomly oriented. Therefore, the substance has zero resultant magnetic moment ( fig 1 ) 21
22. 22. 9011041155 / 9011031155 3. In a weak external magnetic field, the domains having magnetic moment in the direction of the external magnetic field begin to grow in size. There is a shift of the boundaries between the domains and the substance gets magnetized. When the external field is removed, the boundaries return to their original positions and the material looses its magnetism. (Fig. 2) 4. In a strong magnetic field, the domains rotate in the direction of the external magnetic field and the substance gets strongly magnetized. The boundaries vanish forever. When the external field is removed, the domains and their magnetic moments do not return to their original position. ( fig 3 ) This is how the ferromagnetic substances retain their magnetism. 22
23. 23. 9011041155 / 9011031155 Examples :- Iron, nickel, cobalt, steel and their alloys are ferromagnetic in nature. Curie Temperature When a ferromagnetic substance is heated, thermal random motion of the atoms in the domain is enhanced. So, the coupling between the atomic dipoles becomes weak. When the temperature is increased further, at a certain temperature, all these couplings are broken and the domain structure collapses completely and each domain looses its large magnetic moment completely. This temperature at which the domain structure is destroyed completely is called Curie temperature. 23
24. 24. 9011041155 / 9011031155 If the substance is held above the curie temperature, the ferromagnetic substance is converted in to paramagnetic substance, since the force of interaction between the atomic magnets responsible for the ferromagnetism vanishes. Curie temperatures for nickel, iron and cobalt are 360 oC , 770 oC, and 1150 oC respectively. • Ask Your Doubts • For inquiry and registration, call 9011041155 / 9011031155. 24