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ii, Magnetic Materials 12th Science 12th - Physics Syllabus 1. Introduction: 2. Torque Acting on a Magnetic Dipole in a Uniform Magnetic Field 3. Origin of Magnetism in Materials 3.1 Magnetic Moment of an Electron Revolving Around the Nucleus of an Atom 4. Magnetization and Magnetic Intensity 5. Magnetic Properties of Materials 5.1 Diamagnetism 5.2 Paramagnetism 5.3 Ferromagnetism 5.4 Effect of Temperature 6. Hysteresis 7. Permanent Magnet and Electromagnet 8. Magnetic Shielding ‘Theory Notes ; ic Fi i ic for’ O Wnts magnetic eld? | whee tres around a magnet in which magnetic cv of | rienced is called magnetic field. mined from the density 0 | 2) Strength of magnetic field can be determ ee eg of force per Unit | lines of force ie. the number of magnetic ‘el i metic flux : 3) Number of magnetic lines of force is called ae caid be efven | Hence the magnitude of strength of magne! | as magnetic flux per unit area. ce can be expe- magnetic flux magnetic TUX magnetic field = area | = “B= A - unit of Unit of B = Gnit of A. weber (Wb) «SI unit of magnetic field ®) is Wb/m’. or Tesla (T) 1Wb/m’ = 1 Tesla = 10° Gauss(G) Q. What is bar magnet? Bar Magnet 1) Magnet in the form of a bar (rod) is called bar magnet. 2) It has two inseparable poles i.e. north pole with pole strength +qn and south pole with pole strength —qn. ; 3) Separation between two poles inside the magnet is 21. | “Gn +4, 21 Fig. Bar Magnet Q. What is magnetic dipole? Magnetic Dipole How is dipole moment 1) A bar magnet having two poles w: calculated? strengths is called magnetic dipole. 2) Magnetic dipole moment is the product of ma; gnitude of any one pole strength and the separation between two poles. ith equal and opposite pole m= Qn .2T Where m =magnetic dipole moment qn = magnitude of pole strength 27 = separation between two poles 2T isa vector from south pole to north pole 3) SI unit of pole stren ; gth is Ampere meter (Am) and SI unit of magnetic dipole mo ment is Ampere (meter)? Am?, Q. Give the equation for magnetic potential energy stored in a bar magnet placed in uniform external magnetic field. MB V9. (3) s the angular simple harmonic jven by- This equation shows that this i a motion (S.H.M.) analogous to linear S.H.M. g! Gk —_ wy... (4) 7 From equations (3) and (4) gy = 2B a ar] The time period of angular oscillations of the bar magnet will be- _ 2a _ T_ T= = 20 Magnetic potential energy _ Consider a bar magnet having dipole moment m placed ina uniform external magnetic field B as shown below. Let @ be the angle between mand B. Due to the external magnetic field, forces are exerted on the poles of the bar magnet along different lines of action. These forces form a couple that produces rotational motion. The torque acting on the bar magnet will be- v= mBsin0 Due to the displacement, work is done and this work is stored in the form of potential energy in the new position. This is the magnetic potential energy, given as- U, = ['(0)48 Un = [me sind dO Uy =— mB cosO This is the equation for magnetic potential energy. Case 1) If m and B are parallel, = 0°, cos = 0° = | Um =— mB The bar magnet will have minimum potential energy and is in the most stable state. __ Case 2) If m and B are antiparallel, 6 = 180°, cos 180° =— | Uy = mB The bar magnet will have maximum potential energy and is in the most unstable state. Case 3) If m and B are perpendicular, @ = 90°,cos90° = 0 ia = 0 The bar magnet will have zero potential energy. Q. Derive an expression for the magnetic dipole moment of a revolving electron. Q. Show that the orbital magnetic dipole moment of a revolving electron is a (Mar. 14, Mark 2) Q. Ina hydrogen atom, an electron carrying charge e revolves in an orbit of radius r with speed v. Obtain an expression for the magni- tude of the magnetic moment of the revolving electron. (Oct. 14, Mark 2) mB 0 ‘90 180 -mB| Magnetic dipole moment of a revolving electron 1) When a negatively charged electron (—e) revolves around the positively charged nucleus in ator, it performs U.C.M. Ex. Hydrogen atom. m, 2) Let r is the radius of revolution of electron, v is the orbital velocity and 7 is the period of revolution, then- pa 2H Te" 3) The orbital motion of the electron produces a loop of conventional current Jin the opposite direction of its revolution. «. circulating current() = ea wl) 4) The orbital magnetic moment (,) associated with orbital current loop is- Mon = TA... From equations (1) and (2) ev 2 x ar A Mon = 2: ar = evr Je Mon = 2 This magnetic moment is directed towards the plane of paper. Multiplying and dividing RHS by the mass of electron (m.), we get- é€ Mon = > X me = Fin, X Mave & Lace (3) " —& Mow = Fn Where L = m,vr =angular momentum of electron 5) In vector form, —- _e Mom =F Negative sign shows that magnetic moment and angular momentum of electron are oppositely directed. 6) According to the second postulate of Bohr theory of hydrogen atom, the angular momentum of an electron revolving in a circular orbit is integral (7) multiple of (h/2z) th oL= my = 2x xE Therefore equation (3) becomes enh Mors = _ Q. What is the relation between permeability and magnetic susceptibility ofa medium? What is relative permeability of a medium? Q. Define - Magnetism. Write a note on origin of magnetism. Q. Explain origin of diamag- netic on the basis of its atomic structure. Q. Give the properties of diamagnetic substances. Ans. . . If v is the magnetic susceptibility of a medium and / is the perme- ability of the medium, then- w= po(ltx) Where //, is the permeability of free space. i ili i bility of free The ratio of permeability of a medium to the permeabil space is called relative magnetic permeability of the medium (s1,). ut w= = 1+ we Me Io x Magnetism - The property by which the substance can attracts the small pieces of iron is called as magnetism. Origin of Magnetism 1) We know that, whe then the magnetic The circulating electro’ moment. . When electron revolves in the circular orbit, it has two types of motion due to which two types of magnetic moments are produced. ; 3) Orbital magnetic moment is pros ‘ electron and spin magnetic moment is pro motion of electron. ; 4) The resultant magnetic moment of the electron is the vector sum of the orbital and spin magnetic moment. This is the origin of magnetism. n the current passes through the conductor field is produced in the surrounding region. n charges produce the magnetic dipole 2 duced due to orbital motion of duced due to spin of Types of substances on the basis of magnetic properties - On the basis of magnetic properties, substances are classified into three categories as- 1) Diamagnetic substances 2) Paramagnetic substances and 3) Ferromagnetic substances Diamagnetic Substances 1) The substances which are weakly repelled by the magnet are called as diamagnetic substances. The property possessed by diamagnetic substance is known as diamagnetism. 2) Ex. Bismuth, copper, gold, air, zinc, mercury, silver, water, antimony lead, silicon, glass, wood, plastics etc. In diamagnetic substance, the resultant magnetic moment of the atom is zero, because magnetic dipole moments of all the electrons in atom cancel each other. 4) When the diamagnetic substance is placed in external magnetic field, the electrons with orbital magnetic moments in the same direction as that of external field slow down while the electrons with orbital magnetic moments in the opposite direction to that of external field speed up. This develops magnetic moment in the direction opposite to that of external magnetic field and hence the substance is repelled in external magnetic field. 5) The metals, cooled to very low temperature are superconductors and show perfect diamagnetism. This phenomenon is known as Meissner effect. Properties of Diamagnetic Substances 1) If a thin rod of diamagnetic material is suspended freely in uniform magnetic field then it comes to rest perpendicular to the direction of the magnetic field. 2) If a thin rod of diamagnetic material is suspended freely in 3 non-uniform magnetic field then it moves towards the weaker Q. What are paramagnetic subsiances? Enlist the properties of paramagnetic substances. Q. Explain origin of para- mangnetism on the basis of its atomic structure. Q. What are ferromagnetic substances. Give their exam- ples. Write the properties of ferromagnetic substances. tiie U shaped tub i i i cen i shaped tube 3) If the liquid diamagnetic substance 1S taken in ape and magnetic field is applied to one arm then the liquid level decreases in that arm. —— 7 4) Resultant magnetic dipole moment of each atom of diamagnetic substance is zero. se oli 7 5) The permeability (Lt) of diamagnetic substance 1S slightly less than 1. (U<1 : ay 6) The susceptibility (x) of diamagnetic substance is small and negative. Paramagnetic Substances d by the magnet are 1) The substances which are weakly attracte : ays called as paramagnetic substances. The property possessed by the paramagnetic substances is called as paramagnetism. oxygen, platinum, 2) Ex. Aluminium, chromium, magnanese, titanium, sodium, magnesium, lithium, molybdenum ete. 3) In paramagnetic substance, the resultant magnetic moment of atom is not zero, because magnetic dipole moments of sil the electrons in atom do not cancel each other. It has permanent magnetic dipole moment. Each atom of paramagnetic subslance gnets. is equivalent to tiny magnetic dipole called atomic ma ; 4) When a paramagnetic substance is placed in external magnetic field the tiny atomic magnets tend to align parallel to the applied field and show temporary magnetization. When the external field is removed, atomic magnets get randomly oriented and it loses its magnetization. Therefore it cannot be used to make permanent magnets, Properties of paramagnetic Substances 1) If a thin rod of paramagnetic material is suspended freely in uniform magnetic field then it comes to rest parallel to the direction of magnetic field. When a thin rod of paramagnetic material is suspended freely in non uniform magnetic field, then it moves towards the stronger part. 3) If the liquid of paramagnetic substance is taken in U shaped tube and magnetic field is applied to one arm then the liquid level increases in that arm. 4) It possesses Permanent magnetic dipole moment. 5) The permeability (4) of paramagnetic substance is slightly greater than 1. (u =i 6) The Susceptibility (y positive. 2 Jor paramagnetic substance is small and Ferromagnetic Substances 1) The substances which are strongly attracted by the magnet are called as ferromagnetic substances. The property possessed by the ferromagnetic substances is called as ferromagnetism. 2) Ex. Iron, nickel, cobalt, gadolinium, dysprosium and their alloys etc. When a ferromagnetic substance is placed in external field, its magnets get aligned. They retain some magnetism even after removal of external field. Therefore they can be used to make permanent magnets. Properties of Ferromagnetic Substances 1) If a thin rod of ferromagnetic material is placed in uniform magnetic field then it is strongly magnetized in the direction of magnetic field. 2) When a thin rod of ferromagnetic material is placed in non-uni- form magnetic field then it moves from weaker part to the stronger part of the field. 3) Q. Explain the effect of temperature on ferromagnetism. Q. Explain the effect of temperature on ferromagnetism. Q. Explain hysteresis cycle of ferromagnetic materials. Where, . M is magnetization of paramagnetic material B is external magnetic field, T is absolute temperature and C is Curie constant. | We have B= ttoH Ma cla = c# HE £ | Curie Temperature (Effect of Temperature) 1) The temperature above which domain structure of ferromag- netic material is destroyed and ferromagnetic substance loses its magnetism is called as Curie temperature (T) 2) If the temperature of ferromagnetic material is increased then due to thermal vibrations, the coupling between neighbouring moments breaks at certain temperature. 3) At this temperature, almost all the atomic magnets are oriented in all possible direction and due to this, domain structure gets destroyed. This temperature is known as Curie temperature. 4) Above Curie temperature, the ferromagnetic material is converted into paramagnetic substance. 5) The relation between the magnetic susceptibility of a material when it has acquired paramagnetic property and the tempera- ture T is given by - G 7 for T > Te x= T Where C is a constant \<— ferromagnetic paramagnetic Te ™T-~ Hysteresis cycle : . 1) Consider an unmagnetized rod of ferromagnetic material placed inside a solenoid. It is represented by point 'O' in the following graph. B fhox density» ‘ saturation retentivity coercivity # magnetizing force saturationin in opposite direction “flux density in opposte direction Q. Write a note on electromagnet. Q. Write a note on perma- nent magnet. Q, What is magnetic shielding? / _ _ 2) When current is passed through the solenoid, magnetic field is generated and the rod gets magnetized. As the strength of external magnetic intensity H is increased by increasing current, B also increases nonlinearly and point ‘a’ is reached. This is the saturation magnetization point at which magnetic field is maximum. Domains are completely aligned. If H is further increased, there is no increase in B. Now, if H is reduced to zero by reducing current zero, B does not become zero. Thus earlier path is not retraced and point 'b' is reached. This value of B when H=0 is called retentivity or remanence, Some domains are still aligned. 5) Next, when H is increased in reverse direction by increasing current in the reverse direction, point 'c’ is reached, where B=0 at a certain value of H. This value of H is called coercivity. Domains are randomly oriented. . If His further increased in reverse direction, point ‘a’ is reached. This is again the saturation magnetization point at which magnetic field is maximum. If H is further increased, there is no increase in B. 7) Now, if His again reduced to zero by reducing current zero, B does not become zero. Thus earlier path is not retraced and point 'e' ig reached. Domains are again aligned but the direction of magnetization is reversed. . 8) When H is further increased, point | and then point 'a' is reached. Thus one loap is completed. This loop is called hyster- esis loop and the process of taking magnetic material through the loop is called hysteresis cycle. 3 4 6 Electromagnet |, 1) Electromagnet is prepared by placing a soft ferromagnetic rod in a solenoid core. 2) When current is passed through the solenoid, the magnetic field associated with the solenoid increases and the rod gets magnetized. 3) As the soft ferromagnetic material has a very little property to retain magnetization, when the current is switched off, the rod becomes unmagnetized. 4) Electromagnets are used in electric bells, loud speakers, circuit breakers, in cranes etc. Permanent magnet 1) Permanent magnet is prepared by placing a hard ferromagnetic rod in a solenoid core. 2) When current is passed through the solenoid, the magnetic field associated with the solenoid increases and the rod gets magnetized. 3) As the hard ferromagnetic material has a property to retain magnetization, when the current is switched off, the rod remains magnetized. Magnetic shielding 1) Ifa soft ferromagnetic material is placed in a uniform magnetic field, most of the magnetic lines pass through the material. 2) If the instrument which is to be protected from magnetic field is surrounded by a closed structure like a spherical shell of ferro- magnetic material, very few magnetic lines pass through the enclosed space and the instrument is protected. This effect is known as magnetic shielding. 3) Some scientific experiments require the experiment to be protected from magnetic field in the laboratory. 4) This technique is also used in space ships. tl Important Formulae Formula Magnetic dipole moment Explanation M=IA Where For ‘n’ turns M = magnetic dipole moment (Am) Me=nlA T= current in loop (A) Magnetization A= area of loop(m) AM. M, = 44 Lap V = volume (m*) Magnetic susceptibility AM a: . H Magnetic filed in terms of y B=mw(l+x)H x =magnetic susceptibility Relative permeability = (14x) at lt Wh u, =relative permeability When charge ‘e’ revolves in i path with period ‘T’ circular lap M=efrr e = charge (C) T = period (sec) f= frequency (Hz) r= radius (m) ae |Numerical — Text Book (Solved) 1) A bar magnet of moment of inertia of 500 g cm? makes 10 oscillations per minute ina hori- zontal plane. What is its magnetic moment, if the horizontal component of earth s magnetic field is 0.36 gauss? Given: Moment of Inertia I = 500 g cm? Frequency n = 10 oscillation per minute = 10/60 oscillations per second, Time period T = 6 sec, B,, = 0.36 gauss. 2) Calculate the gyromagnetic ratio of electron (given e = 1.6 X 10°’ C,me = 9.1 x 10 “"kg) 3) The region inside a current carrying toroid winding is filled with Aluminium having suscep- tibility x = 2.3 X 10°. What is the percentage increase in the magnetic field in the presence of Aluminium over that without it? 4) A domain in ferromagnetic iron is in the form of cube of side lum. Estimate the number of iron atoms in the domain, maximum possible dipole moment and magnetisation of the domain. The molecular mass of iron is 55 g/mole and density is 7.3 g/cm’. Assume that each iron atom has a dipole moment of 9.27 X 10°'Anr. 
