Applied Physics Unit 3 Notes PDF

Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE UNIT – III: MAGNETIC MATERIALS AND SUPURCONDUCTIVITY MAGNETIC MATERIALS Introduction: The basic aim in the study of the subject of magnetic materials is to under...

Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE UNIT – III: MAGNETIC MATERIALS AND SUPURCONDUCTIVITY MAGNETIC MATERIALS Introduction: The basic aim in the study of the subject of magnetic materials is to understand the effect of an external magnetic field on a bulk material, and also to account for its specific behavior. A dipole is an object that a magnetic pole is on one end and a equal and opposite second magnetic dipole is on the other end. Magnetic materials are those which can be easily magnetized as they have permanent magnetic moment in the presence of applied magnetic field. Magnetism arises from the magnetic dipole moments. It is responsible for producing magnetic influence of attraction or repulsion. Magnetic dipole: It is a system consisting of two equal and opposite magnetic poles separated by a small distance of ‘2l’metre. Magnetic Moment (μm ): It is defined as the product of the pole strength (m) and the distance between the two poles (2l) of the magnet. i.e. μm = m ×2l Units: Ampere – metre2 In case of current carrying conductor, it is the product of Current (i) and cross-section area (A) of the conductor (In case of atom, it is the product of current (i) developed by the orbital motion of electron and the area covered by the orbital, i.e. μm = i.A Magnetic Flux Density or Magnetic Induction (B): It is defined as the number of magnetic lines of force passing perpendicularly through unit area. i. e. B = magnetic flux / area = Φ / A Units: Weber / metre2 or Tesla (T). Permeability: Magnetic Field Intensity (H): The magnetic field intensity at any point in the magnetic field is the force experienced by a unit north-pole placed at that point. Units: Ampere / meter (Am-1) The magnetic induction B due to magnetic field intensity H applied in vacuum is related by B = μo H where μo is permeability of free space = 4 Π x 10-7 Hm-1 If the field is applied in a medium, the magnetic induction in the solid is given by B = μ H where μ is permeability of the material in the medium μ=B/H Hence magnetic Permeability μ of any material is the ratio of the magnetic induction to the applied magnetic field intensity. GRIET Page 39 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE Relative Permeability (μo): The ratio of μ / μo is called the relative permeability (μr ) μr = μ / μo Therefore, B = μo μrH Magnetization(M): It is the process of converting a non – magnetic material into a magnetic material. The magnetization (M) of a material is the magnetic moment per unit volume. i.e. M= μm/V Magnetic susceptibility (χ): The magnetization is directly related to the applied field H through the susceptibility of the medium (χ) by χ = M / H ------------ (1) The magnetic susceptibility of a material is the ratio of the intensity of magnetization produced to the magnetic field intensity which produces the magnetization. It has no units. We know i.e B = μo ( H + M )---------- (2) The first term on the right side of eqn. (2) is due to external field. The second term is due to the magnetization. Hence, 𝜇 = Relative Permeability, 𝜇 = = = =1+ 𝑴 𝝁𝒓 = 𝟏 + 𝝌 ∵𝝌= 𝑯 ORIGIN OF MAGNETIC MOMENT: BOHR MAGNETON The magnetic properties of all substances are associated with the orbital and spin motions of the electrons in their atoms. Due to this motion, the electrons become elementary magnets of the substance. In few materials these elementary magnets are able to strengthen the applied magnetic field, while in few others, they orient themselves such that the applied magnetic field is weakened. Electricity is the movement of electrons, whether in a wire or in an atom, so each atom represents a tiny permanent magnet in its own right. The circulating electron produces its own orbital magnetic moment, measured in Bohr magnetrons (µB) and there is also a spin magnetic moment associated with it due to the electron itself spinning on its own axis. GRIET Page 40 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE The magnetic moment contributed by a single electron is known as Bohr magnetron. Mathematically, it can be expressed as 1𝜇 = Proof: Let an electron of charge e is moving in an orbital of radius r around a nucleus with a velocity 𝑣 is shown in figure. Hence, the current constituted will be, 𝑖 = or 𝑖= ------------(1) Where, T is time for one revolution of electron about the nucleus, i.e., 𝑇= ------------ (2) Where ω is the angular velocity of electron. Therefore, 𝑇 = (since v = rw) The definition of dipole-moment, say that, 𝜇 = 𝑖. 𝐴 ---------------(3) From eqn’s (1), (2) and (3), we get, 𝜇 = (𝜋𝑟 ) Since area covered by the orbital, A= πr2 ( ) or 𝜇 = ------------- (4) But, the angular momentum of the electron is, 𝐿 = 𝑚𝑣𝑟 = = 𝑙ℏ 𝑠𝑖𝑛𝑐𝑒 ℏ = ------- (5) Substituting eqn (5) in eqn (4), we get, ℏ 𝜇 = − 𝑙 ℏ ⟹ 𝜇𝑚 = −𝝁𝑩 𝑙 ∵ = 𝝁𝑩 ℏ The quantity, = 𝝁𝑩 is called Bohr magneton and has a value of 9.27 × 10-27 A-m2. The negative sign here indicates that magnetic moment is anti-parallel to the angular momentum. GRIET Page 41 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE CLASSIFICATION OF MAGNETIC MATERIALS: All matter responds in one way or the other when subjected to the influence of a magnetic field. The response could be strong or weak, but there is none with zero response i.e., there is no matter which is nonmagnetic in the absolute sense. Depending upon the magnitude and sign of response to the applied field, and also on the basis of effect of temperature on the magnetic properties, all materials are classified broadly under three categories. 1. Diamagnetic materials 2. Paramagnetic materials, 3. Ferromagnetic materials Two more classes of materials have structure very close to ferromagnetic materials but possess quite different magnetic effects. They are 4. Anti-ferromagnetic materials and 5. Ferri magnetic materials 1. DIA 2. PARA 3. FERRO i Diamagnetic substances are Paramagnetic substances are Ferromagnetic substances are those substances which are those substances which are those substances which are feebly repelled by a magnet. feebly attracted by a magnet. strongly attracted by a magnet. Ex.: Cu, Au, Ag, Hg, Water, Ex.: Al, Cr, Alkali and rare Ex.: Fe, Co, Ni, Gd, Dy, etc Hydrogen, Air, Argon, etc., earth metals, Pt, Oxygen, etc. ii When placed in magnetic The lines of force prefer to The lines of force tend to crowd field, the lines of force tend to pass through the substance into the specimen. avoid the substance. rather than air. GRIET Page 42 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE iii When a diamagnetic rod is When a paramagnetic rod is When a ferromagnetic rod is freely suspended in a uniform freely suspended in a uniform freely suspended in a uniform magnetic field, it aligns itself magnetic field, it aligns itself magnetic field, it aligns itself in in a direction perpendicular to in a direction parallel to the a direction parallel to the field the field. field. very quickly. iv If diamagnetic liquid taken in If paramagnetic liquid taken If Ferromagnetic liquid taken in a watch glass is placed in in a watch glass is placed in a watch glass is placed in uniform magnetic field, it uniform magnetic field, it uniform magnetic field, it collects away from the centre collects at the centre when the collects at the centre when the when the magnetic poles are magnetic poles are closer and magnetic poles are closer and closer and collects at the centre collects away from the centre collects away from the centre when the magnetic poles are when the magnetic poles are when the magnetic poles are farther. farther. farther. v It is weakly magnetized in the It is weakly magnetized in the It is Strongly magnetized in the opposite direction of the field direction of the field (H) direction of the field (H) (H) vi Induced Dipole moment (μm) Induced Dipole moment (μm) Induced Dipole moment (μm) and Magnetization (M) are and Magnetization (M) are and Magnetization (M) are small -ve value small +ve value large +ve value vii Magnetic permeability μ is Magnetic permeability μ is Magnetic permeability μ is large always less than unity. more than unity. and larger than unity. viii Magnetic Susceptibility ᵡm has Magnetic Susceptibility ᵡm Magnetic Susceptibility ᵡm has a a small and –ve value has a small and +ve value large and +ve value ix They do not obey Curie’s law, They obey Curie’s law. They They obey Curie’s law. At i.e. Their properties do not lose their magnetic properties certain temperature, called change with temperature. with rise in temperature. Curie point, they lose ferromagnetic properties and behave like paramagnetic GRIET Page 43 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE substances. x 4. Anti-ferromagnetic materials: These are the ferromagnetic materials in which equal no of opposite spins with same magnitude such that the orientation of neighboring spins is in antiparallel manner are present.  Susceptibility is small and positive and it is inversely proportional to the temperature.  Susceptibility, 𝜒 = , ↑↓↑↓↑↓↑↓ TN – the temperature at which anti-ferromagnetic material converts into paramagnetic material is known as Neel’s temperature.  Ex: FeO, Cr2O3, etc., 5. Ferri-magnetic Materials: These are the ferromagnetic materials in which equal no of opposite spins with different magnitudes such that the orientation of neighboring spins is in antiparallel manner are present.  Susceptibility positive and large, it is inversely proportional to temperature.  Susceptibility, 𝜒 = ± , T>TN (Neel’s Temperature) ↑ ↓↑ ↓↑ ↓↑ ↓  Ex.: Fe2O4, ZnFe2O4, CuFe2O4, etc., DOMAIN THEORY OF FERROMAGNETISM: According to Weiss, a virgin specimen of ferromagnetic material consists of a no of regions or domains (≈ 10–6 m or larger) which are spontaneously magnetized. In each domain spontaneous magnetization is due to parallel alignment of all magnetic dipoles. The direction of spontaneous magnetization varies from domain to domain. The resultant magnetization may hence be zero or GRIET Page 44 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE nearly zero. When an external field is applied there are two possible ways of alignment for a random domain. i). By motion of domain walls: The volume of the domains that are favorably oriented with respect to the magnetizing field increases at the cost of those that are unfavorably oriented. ii) By rotation of domains: When the applied magnetic field is strong, rotation of the direction of magnetization occurs in the direction of the field. HYSTERESIS LOOP (B-H or M-H CURVE): Hysteresis is the dependence of the state of a system on its history. 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 magnetic flux density (B) and the applied magnetic field (H). It is often referred to as the B-H loop. An example hysteresis loop is shown. The loop is generated by measuring the magnetic flux of a ferromagnetic material while the applied magnetic field 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. GRIET Page 45 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE As the line demonstrates, the greater the amount of field applied (H+), the stronger the magnetic field in the component (B+). At point "a" almost all of the magnetic domains are aligned and an additional increase in the magnetic field (H) will produce very little increase in magnetic flux. The material has reached the point of magnetic saturation. When H is reduced to zero, the curve will move from point "a" to point "b." At this point, it can be seen that some magnetic flux 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 some have lost their alignment.) As the magnetizing force is reversed, the curve moves to point "c", where the flux has been reduced to zero. This is called the point of coercivity on the curve. (The reversed magnetizing force has flipped enough of the domains so that the net flux within the material is zero.) The force (field) required to remove the residual magnetism from the material is called the coercive field or coercivity of the material. As the magnetizing force 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 force is required to remove the residual magnetism. The curve will take a different path from point "f" back to the saturation point where it will complete the loop. From the hysteresis loop, a number of primary magnetic properties of a material can be determined. i. Retentivity: It is the materials ability to retain a certain amount of residual magnetic flux when the magnetic field is reached to zero. (The value of B at point “b” on the hysteresis curve.) ii. Residual Magnetism or Residual Flux: The magnetic flux that remains in a material when the magnetizing force is zero. iii. Coercive Field: The amount of reverse magnetic field which must be applied to a magnetic material to make the residual magnetic flux return to zero. (The value of H at point “c” on the hysteresis curve). GRIET Page 46 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE SOFT AND HARD MAGNETIC MATERIALS: Hysteresis loop of the ferromagnetic materials vary in size and shape. This variation in hysteresis loops leads to a broad classification of all the magnetic materials into hard and soft magnetic materials. i. Soft magnetic materials: Soft magnetic materials are also called as permeable magnetic materials, since they can be easily magnetized and also demagnetized. Ex.: Soft iron, Si-Fe alloy, Permalloys (Alloys of Fe and Ni), etc., Properties: 1. High permeability, 2. High susceptibility, 3. Low coercivity, 4. Low retentivity, 5. High saturation magnetization, 6. Low hysteresis energy loss. Applications:1. They are used in electromagnets, 2. They are used in communication equipments, and 3. They are used in audio and video transformers. ii. Hard magnetic materials: Hard magnetic materials are also called as permanent magnetic materials because they cannot be magnetized and demagnetized very easily. Ex.: Alnico alloy, Cu-Ni-Fe alloy, Ni steel, etc., Properties: 1. Low permeability, 2. Low susceptibility, 3. High coercivity, 4. High retentivity, 5. Low saturation magnetization, 6. High hysteresis energy loss (area under the curve). Applications: 1. They are used in digital computers, 2. They are used for making permanent magnets, and 3. They are used in transducers and magnetic tapes. GRIET Page 47 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE S.No. Soft magnetic materials Hard magnetic materials Soft magnetic materials have low Hard magnetic materials have large i. hysteresis loss due to small hysteresis hysteresis loss due to large hysteresis is loop loop area area. In these materials the domain wall In these materials the domain wall movement is relatively easier, even movement is difficult because of presence ii. for small changes in the magnetizing of impurities and crystal imperfection and it field the magnetization changes by is irreversible in nature. large amount. The coercivity and retentivity are The coercivity and retentivity are large. small. Hence, these materials can be Hence these materials cannot be easily iii. easily magnetized and demagnetized. magnetized and demagnetized These materials are free from In these materials, because of the presence irregularities; the magneto static of impurities and crystal imperfection the iv. energy is small. mechanical strain is more. Hence magneto static energy is large. These materials have large values of These materials have small values of v. susceptibility and permeability. susceptibility and permeability These are used to make electronic These are used to make permanent magnets vi. magnets. Applications: Mainly used in Applications: For production of permanent electromagnetic machinery and magnets used in magnetic detectors, transformer cores. They are used in microphones flux meters, voltage vii. switching circuits, microwave regulators, damping devices, magnetic insulators and matrix storage of separators, and loud speakers. computers. Applications of Magnetic Materials: Magnetic materials are surprisingly common in our everyday lives, even if we don't always notice them. Here are some simple applications: 1. Refrigerator Magnets: These are a classic example. They stick to your fridge and can hold notes, photos, or even just serve as decorations. 2. Credit Cards and ID Badges: Many credit cards and ID badges use magnetic strips to store information. The magnetic material is used to encode data that can be read by machines. 3. Electric Motors: Found in everything from household appliances to toys, electric motors use magnets to create rotational motion. This includes fans, blenders, and even some power tools. 4. Speakers and Headphones: These devices use magnets to convert electrical signals into sound. In speakers, the magnet interacts with a coil to move a diaphragm, producing sound waves. GRIET Page 48 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE 5. Magnetic Locks: Often used in office buildings or secure areas, magnetic locks rely on electromagnetic forces to keep doors locked until a magnetic key or card is used. 6. Magnetic Compasses: Used in navigation, compasses use Earth's magnetic field to show direction. This principle is also employed in some modern GPS devices for orientation. 7. Magnetic Toys: Many children's toys, like magnetic building blocks or games, use magnets to allow pieces to stick together or interact in specific ways. 8. Microwave Ovens: Inside a microwave, a magnetron uses magnetic fields to generate microwave radiation, which heats your food. 9. Medical Devices: Magnetic resonance imaging (MRI) machines use strong magnets to create detailed images of the inside of the body, aiding in medical diagnoses. 10. Magnetic Fasteners: Used in clothing, bags, and other accessories, these fasteners rely on magnets to stay securely closed. GRIET Page 49 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE SUPERCONDUCTIVITY Certain metals and alloys exhibit almost zero resistivity (i.e. infinite conductivity) when they are cooled to sufficiently low temperatures. This phenomenon is called superconductivity. This phenomenon was first observed by H.K. Onnes in 1911. He found that when pure mercury was cooled down to below 4K, the resistivity suddenly dropped to zero. Since then hundreds of superconductors have been discovered and studied.  Superconductivity is strictly a low temperature phenomenon.  Few new oxides exhibited superconductivity just below 125K itself.  This interesting phenomenon has many important applications in many emerging fields. Critical Temperature (Tc): The temperature at which the transition from normal state to superconducting state takes place on cooling in the absence of magnetic field is called the critical temperature or the transition temperature. General Properties: The following are the general properties of the superconductors: 1. The transition temperature is different to different substances. 2. For a chemically pure and structurally perfect specimen, the superconducting transition is very sharp. 3. Superconductivity is found to occur in metallic elements in which the number of valence electrons lies between 2 and 8. 4. Transition metals having odd number of valence electrons are favorable to exhibit superconductivity while metals having even number of valence electrons are unfavorable. 5. Materials having high normal resistivities exhibit superconductivity. 6. Materials for which Zρ > 106 (where Z is the no. of valence electrons and ρ is the resistivity) show superconductivity. 7. Ferromagnetic and antiferromagnetic materials are not superconductors. GRIET Page 50 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE 8. The current in a superconducting ring persists for a very long time. MEISSNER EFFECT: When a weak magnetic field applied to a superconducting specimen at a temperature below transition temperature Tc, the magnetic flux lines are expelled. The specimen acts as on ideal diamagnet. This effect is called Meissner effect. This effect is reversible, i.e. when the temperature is raised from below Tc, at T = Tc the flux lines suddenly start penetrating and the specimen returns to the normal state. Under this condition, the magnetic induction inside the specimen is given by, B = µo(H + M) ---------------------------- (1) Where H is the external applied magnetic field and M is the magnetization produced inside the specimen. When the specimen is super conducting, according to Meissner effect, inside the bulk semiconductor, B= 0. Hence µo(H + M) = 0 or H + M = 0, (Since, µo ≠0) H= - M or = −1 𝜒 = −1 ∵𝜒= ------ (2) Thus, the material is perfectly diamagnetic. According to Meissner effect perfect diamagnetism is an essential property of defining the superconducting state. Thus, From zero resistivity, E = 0, From Meissner effect, B= 0. GRIET Page 51 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE TYPE- I AND TYPE- II SUPERCONDUCTORS: Based on diamagnetic response, Superconductors are divided into two types, i.e type-I and type- II. i. Type-I superconductors: Superconductors exhibiting a complete Meissner effect are called type-I, also called Soft superconductors. When the magnetic field strength is gradually increased from its initial value H< HC, at HC the diamagnetism abruptly disappears and the transition from superconducting state to normal state is sharp. Ex.: Zn, Hg, pure specimens of Al and Sn. ii. Type-II superconductors: In type-II Superconductors, transition to the normal state takes place gradually. For fields below HC1, the material is diamagnetic i.e., the field is completely excluded. HC1 is called the lower critical field. At HC1 the field begins to penetrate the specimen. Penetration increases until HC2 is reached. At HC2, the magnetizations vanishes i.e., the material becomes normal state. HC2 is the upper critical field which is equal to 100 times of Hc. Between HC1 and HC2 the state of the material is called the mixed or vortex state. They are also known as hard superconductors. They have high current densities. Ex.: Zr, Nb, Nb3Ge, Nb3Si, YBa2Cu3O7, etc APPLICATIONS OF SUPERCONDUCTORS: 1. Magnetic levitation:  Magnetic levitation, magLev, or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields. Magnetic force is used to counteract the effects of the gravitational and any other accelerations. GRIET Page 52 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE Magnetically levitated vehicles are called Maglev vehicles A typical diagram of Maglev train is shown in the Figure. The train has superconducting magnets built into the base of its carriage. An aluminium guideway is laid on the ground and carries current. The repulsion between the two powerful magnetic fields, namely the field produced by the superconductor magnet and the field produced by the electric current in the aluminium guideway causes magnetic levitation of the train. The train is fitted with retractable wheels i.e. when the train is levitated in air, the wheels are retracted into the body and the train guides forward on the air cushion. When the train is to be halted, the wheels are drawn out and the train descends slowly onto the guideway and runs forward till it stops. 2. Smart magnets: Superconducting materials are used for producing very high magnetic fields of the order of 50 Tesla. To generate such a high field, power consumed is only 10 kW, whereas in conventional method for such a high field power generator consumption is about 3 MW. Moreover, in conventional method, cooling of copper solenoid by water circulation is required to avoid burning of coil due to Joule heating. 3. Transmission lines: Since the resistance is almost zero at superconducting phase, the power loss during transmission is negligible. Hence electric cables are designed with superconducting wires. If superconductors are used for winding of a transformer, the power losses will be very small. Questions: Short answer questions: 1. Define the terms a) Magnetic flux b) Magnetic induction c) Magnetic field strength d) Intensity of magnetization e) Magnetic susceptibility f) Magnetic permeability. 2. List the different types of magnetic materials. GRIET Page 53 Applied Physics I B. Tech CSE(AIML)/CSE(DS)/CSE/ECE/EEE/CSBS/ME/CE 3. What is the origin for magnetic moment? 4. What are ferrites? Mention any two applications. 5. What are soft and hard magnetic materials. Long answer questions: 1. Explain the Origin of magnetic moment and derive the expression for Bohr magneton. 2. Explain the classification of magnetic materials on the basis of magnetic moment and mention the properties of various magnetic materials. 3. Examine how the domain theory of ferromagnetism explains the hysteresis curve in magnetic materials. 4. Write a short note on soft and hard magnetic materials. Or distinguish soft and hard magnetic materials. 5. Demonstrate how the Meissner effect can be observed in a superconducting material. 6. Summarize the key differences between Type I and Type II superconductors. 7. List few common applications of superconductors. GRIET Page 54