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THE UNIVERSE AND ENERGY The entire universe is composed of Energy and Energy alone. However, this energy comes in two forms in the known universe. (i) Matter and (ii) Electromagnetic Radiation. We all know what matter isโฆ You and me, dogs, cats, birds, the planets, the sun, the stars, asteroids, the earth, the bus, the car the table, the buildings and every material object that you can think about is matter! They all have an energy stored in them given by the equation E = mc 2 where m is the mass of the object that you are talking about and c the speed of light. Electromagnetic Radiation is the second form of energy it happens as a result of the pulsing forward of oscillating Electric and Magnetic Fields. Quantum Mechanics has now proved that waves sometimes behave like a particle and such a particle that represents a wave is called a photon1. One photon has an energy given by E = hฮฝ which of course is the where ๐ is the frequency of the wave and h is the Planckโs constant2. TRANSVERSE NATURE OF ELECTROMAGNETIC RADIATION As of now, we are going to deal with the wave properties of EM Radiations hence the name Wave Optics. The figure below shows how an Electromagnetic wave propagates in space. In the figure, we see clearly that the electric field vibrates along the x-y plane as ๐ธ(๐ฅ, ๐ก) = ๐ธ0 ๐ ๐๐(๐๐ฅ + ๐๐ก) and the Magnetic Field vibrates along the x-z plane ๐ต(๐ฅ, ๐ก) = ๐ต0 sin(๐๐ฅ + ๐๐ก) and the wave itself propagates forward perpendicular to these two vibrations, along the x axis. Here, ๐ธ(๐ฅ, ๐ก) and ๐ต(๐ฅ, ๐ก) are the instantaneous values of Electric Field and Magnetic Field3 at given values of x and t, E0 and B0 are the maximum values of ๐ธ(๐ฅ, ๐ก) and ๐ต(๐ฅ, ๐ก), ๐ = 2๐๐ where f is frequency of oscillation and k is the wave number4 given ๐ = 2๐/๐. When the vibrating particles of the medium are perpendicular to the direction of propagation, such a wave is called a Transverse wave. Our job now is to prove that Light is indeed a transverse wave. 1 Photon is a particle with zero rest mass consisting of a quantum of em radiation. The photon may also be regarded as a unit of energy hฮฝ 2 Remember that this is only Energy of one photon. The total Energy of the wave depends on its intensity. More the intensity, more the number of photons and hence the total energy will be the sum of the individual energies of all the photons. 3 This representation of E(x,t) is just like putting f(x) showing that the value of Electric field E(x,t) is a function of the x space coordinate and time or in other words, E depends on x and t. If you want the value of E at time say ๐ฅ = 5 ๐๐๐ก๐๐๐ ๐๐๐ ๐ก = 2 ๐ ๐๐๐๐๐๐ , put it in the equation and we get the value E(5,2) = E0 sin(5k + 2ฯ). Similar is the case for B(x,t) 4 Wave Number is the number of waves in unit length times 2๐ 1 qed_amk_gesXII1011 The Proofโฆ Let us consider a plane electromagnetic wave propagating along the X axis. The wave front will be a plane one parallel to YZ plane (see figure below). For any position of the wave front, the electric and magnetic fields E and B will be zero to the right of the wave front because the wave has not reached there yet, while to the left of it, it will depend on x (space โ where we are talking about) and t (time โ when we are talking about) but not on y and z as we are considering a pane wave. To establish the transverse nature of EM waves, we shall show that E and B are perpendicular to the direction of propagation of the wave. Consider an elementary cuboid ABCDPQRS with sides๐ด๐ = ๐๐ฅ, parallel to the X axis, ๐ด๐ต = ๐๐ฆ, parallel to the Y axis, and ๐ต๐ถ = ๐๐ง, parallel to the Z axis. Suppose the wave front reaches the face PQRS at a given time, say t. The fields E and B are zero to the right of PQRS (because the wave has not reached there yet) while to the left of PQRS, the values depend only on x (because we have just now define that we are looking at this matter at a value of time = t). Since the cuboid does not enclose any charge, according to Gaussโ Law, for electricity, the total electric flux through all its six faces must be zero. Mathematically speaking we have, โฎ ๐ฌ โ ๐๐จ = 0 โน โซ ๐ฌ โ ๐๐จ + ๐ด๐ต๐ถ๐ท [(๐ต๐๐๐) โซ ๐ฌ โ ๐๐จ + ๐๐๐ ๐ (๐น๐๐๐๐ก) โซ ๐ฌ โ ๐๐จ + ๐ด๐ต๐๐ (๐ ๐๐โ๐ก) โซ ๐ฌ โ ๐๐จ + ๐ท๐ถ๐ ๐ (๐ฟ๐๐๐ก) โซ ๐ด๐ท๐๐ (๐ต๐๐ก๐ก๐๐) ๐ฌ โ ๐๐จ + โซ ๐ฌ โ ๐๐จ = 0 ๐ต๐ถ๐ ๐ (๐๐๐) ] Since the value of E does not vary with y, the electric flux through the top (BCRQ) and bottom (ADSP) faces normal to the Y axis are equal and opposite and hence the contribution of these two integrals in the above equation cancel each other. Similarly, the flux through the two side faces ABQP (Right) and DCRS (Left) also cancel each other as the E does not vary with the value of z. What is the meaning of E does not depend on y and z?. Strictly speaking, the Electric Field Vector E must be written as ๐ฌ(๐ฅ, ๐ฆ, ๐ง, ๐ก), telling us that the value of E is a function of space coordinates (x, y and z) and of the time coordinate t. If you still donโt understand, remember that to specify the position of an object, we need 4 coordinates x, y, z, and t. Say for example, how do we spot a plane flying somewhere above the surface of the Earth? We need the Latitude (x axis), Longitude (y axis), Altitude (z axis) and also the time of the day (t axis). Hence we say that the position of that plane is a function of space (x, y and z) and time (t). So we write, say, Position of Plane is ๐(๐ฅ, ๐ฆ, ๐ง, ๐ก). Similarly, here we are talking about the instantaneous value of Electric Field of an Electromagnetic wave of frequency f given by ๐ธ(๐ฅ, ๐ฆ, ๐ง, ๐ก). But since the Wave is oscillating along the x axis, it is independent of y and z values and so reduces to ๐ธ(๐ฅ, ๐ก). Same is the case for ๐ต(๐ฅ, ๐ก) Hence the equation reduces to the followingโฆ โซ ๐ฌ โ ๐๐จ + ๐ด๐ต๐ถ๐ท โซ ๐ฌ โ ๐๐จ = 0 ๐๐๐ ๐ [(๐ต๐๐๐) ] (๐น๐๐๐๐ก) โฒ Let ๐ธ๐ฅ and ๐ธ๐ฅ be the values of the x component of E at the faces ABCD (Back) and PQRS (Front) respectively. Then we will have, 2 qed_amk_gesXII1011 โซ ๐ฌ โ ๐๐จ = โ[๐ธ๐ฅ (๐๐ฆ. ๐๐ง)] โซ ๐ฌ โ ๐๐จ = +[๐ธ๐ฅโฒ (๐๐ฆ. ๐๐ง)] & ๐ด๐ต๐ถ๐ท (๐ต๐๐๐) ๐๐๐ ๐ (๐น๐๐๐๐ก) The negative sign in the first equation only indicates that the E and dA are in opposite direction. From the above three equations, we conclude that โซ ๐ฌ โ ๐๐จ + ๐ด๐ต๐ถ๐ท [(๐ต๐๐๐) โซ ๐ฌ โ ๐๐จ = 0 ๐๐๐ ๐ (๐น๐๐๐๐ก) โน โ[๐ธ๐ฅ (๐๐ฆ. ๐๐ง)] + [๐ธ๐ฅโฒ (๐๐ฆ. ๐๐ง)] = 0 ] โน [๐ธ๐ฅโฒ (๐๐ฆ. ๐๐ง)] โ [๐ธ๐ฅ (๐๐ฆ. ๐๐ง)] = 0 โน [๐ธ๐ฅโฒ ] โ [๐ธ๐ฅ ] = 0 This relation says that ๐ธ๐ฅโฒ โ ๐ธ๐ฅ = 0. This leaves us with two possibilitiesโฆ ๐ธ๐ฅโฒ = ๐ธ๐ฅ or ๐ธ๐ฅโฒ = 0 & ๐ธ๐ฅ = 0. The first possibility of ๐ธ๐ฅโฒ = ๐ธ๐ฅ would mean that the electric field is uniform. But a uniform field cannot propagate a wave of finite wavelength according to Maxwellโs Theory. Hence the only possibility is that both ๐ธ๐ฅโฒ & ๐ธ๐ฅ are separately zero. This proves that there is no component of the electric field parallel to the direction of propagation. A very similar argument will hold true for the magnetic field B also. Hence we have proved that in an electromagnetic wave, both Electric and Magnetic field are perpendicular to the direction of propagation, that is, Electromagnetic Wave is a Transverse Wave Remember the following relation where c is the speed of light in vacuum, v is the speed of light in a medium, ฮผ0 is the permeability of free space, ฮผr is the relative permeability, ฮต0 is the permittivity of free space and ฮตr is the relative permittivity of the medium or the Dielectric constant. In vacuum, c= 1 โฮผ0 ฮต0 In any medium, v=( v=( 1 โ(ฮผ0 ฮผr )(ฮต0 ฮตr ) )=( 1 ) โฮผฮต 1 1 c )( )=( ) ฮผ ฮต ฮผ โ r ฮตr โฮผ0 ฮต0 โ r r c c v=( ) โน โฮผr ฮตr = = n v ฮผ ฮต โ r r Where n is the absolute refractive index (with respect to vacuum) of the medium under consideration so, n = โฮผr ฮตr 3 qed_amk_gesXII1011 MODULATION AND DEMODULATION (Syllabus Saysโฆ Modulation and Demodulation โ quantitative only, Amplitude Modulation (AM), Frequency Modulation (FM). Production and Detection, Uses) Modulation is a word often used in Musical terminology. When you say that a song modulates from one pitch to another, it means that the song changes the key or the scale (say G major scale to D major scale). For those of you who donโt understand this, it means that you change you range of frequencies from one to another. Say if I was using a range of 250Hz to 500Hz, I shift to using 350Hz to 700Hz instead. Such a change of frequency is called as modulation. One can also modulate the amplitude (loudness) of ones singing. In the context of ISC, (although this topic is a pain in the neck), we have to talk about the idea of modulation of EM waves and why we do it. When a teacher speaks in a class room, he or she is heard because the sound waves produced in her vocal chords will disturb the air around her mouth and that disturbance will travel in air just like waves on a water surface. However, if you are far away you donโt hear the teacher as loudly as you do when you are close by. This happens as a result of the conservation of Energy. WHAT? Yesโฆ This because the wave spreads out, the same energy has to be spread over a larger area, so the energy at a given area reduces. So, the wave โfizzles outโ just as a water wave fizzles out at distances far away from its source. So naturally, communication over large distances is not possible without the use of technology. You cannot stand in an open ground and shout out โI LOVE YOUโ and expect your girlfriend or boyfriend to hear you! Rajnikanth may do thatโฆ but surely not humans like us. So let us explore how technology is used to achieve communication over large distances. As we all know, any audible audio signal is only of the order of 20Hz to 20,000Hz. To transmit this over a large distance, the following setup is made5. The input analogue signal is received by a microphone that coverts the spoken sound or music or whatever it is into a digital signal (voltages and currents). This is fed into an amplifier that amplifies the signal (the voltage or current) and sends it to an antenna that transmits the signal as an electromagnetic wave into space. The arrangement so far is called a Transmitter. The electromagnetic signal travelling in free space at the speed of light is intercepted by another antenna at the receiving end. It is then fed into an amplifier and finally to a loud speaker which converts the electrical signal back into the original sound signal. This arrangement constitutes a Receiver. This kind of communication system suffers from two drawbacksโฆ (i) The Audio Frequency (20Hz โ 20000Hz) signals have small power and so cannot be effectively radiated to very long distances. (ii) There is not just one transmitter and one receiver in the world. So when different transmitters send signals of different frequencies simultaneously, confusion is created at the receiver due to interference of the different signals. These drawbacks are overcome by making some modificationsโฆ (i) The Audio Frequency (AF) signal or message or wave 6 is superimposed on a Radio Frequency Wave 7 before transmission. This process is known as MODULATION. The high frequency signals can be radiated to very long distances with comparatively less power). (ii) Different transmitting stations are allotted different frequencies for transmission. A single receiver can be tuned to pick up any desired frequency. 5 Remember that in electronics and communication science, we use some terminology that may confuse you. For example, we may say โAudio Signalโ or โInput Signalโ or โAudio Informationโ, or โInput Informationโ. All this means the same thingโฆ and what is it? When you speak on the phone, what you speak is converted to bits of information and this IS the โAudio Signalโ or โInput Signalโ or โAudio Informationโ, or โInput Informationโ. Similarly we have Output Signal of Output Information. So donโt get confusedโฆ 6 Signal or Wave or Message all means the same thingโฆ So donโt get confused. It is in general called as Informationโฆ Audio information, video information etc. 7 This Radio Frequency Wave as you know is an electromagnetic wave and s also known as a CARRIER WAVE and the AF Signal (informationโฆ the digital version of my voice and Rehmanโs voice) is also known as Modulating signal or Modulating wave 4 qed_amk_gesXII1011 Ok what does all this mean? Due to our time constraint, you need to understand only what happens and not how it happensโฆ Let us say that I am singing on the radio in Kerala and it is transmitted all around the world (Ya rite!). But there is also AR Rehman singing in Chennai and that is being aired at the exact same time all around the world. But you see, surely, people love to hear me more that they love to hear Mr. Rehman. So how does one go about sorting this confusion? Surely you donโt want my sound to be mixed with hisโฆ This can be quite an insult for him (or is it for me๏?)! I am singing at a radio station in Trivandrum and Rehman at Chennai. So what the communication department of the country does is to allot specific radio frequencies to the Trivandrum Tower (say 93.5MHz FM) and to the Chennai Tower (say 103.5 MHz FM8). The idea now is to mix (modulate) my sound signal with this 93.5 MHz and to mix Rehmanโs voice with 103.5MHz in a certain manner so that when it reaches your radio, (which has a tunable amplifier) you have the choice of tuning to 93.5 or to 103.5. If you choose 93.5, (which of course is the smart thing to do) then the radio will catch onto this mix of 93.5 Hz and my voice and โunmixโ (demodulate9) it. This ensures that the amplifier in your radio can catch onto only my voice and amplify it so that you can hear my sweet, lovely voice! If your radio on the other had is tuned to 103.5 (not a very smart thing to do though) then Rehmanโs voice is demodulated and you hear that in your radio. So here we have the definitionsโฆ Modulation: It is the super imposing of an Audio Frequency (AF) Input Signal with a Radio Frequency (RF) Wave10 before transmission of the wave over large distances. This is done so that there is efficient transmission of the signal without loss of information. Demodulation: It is the reverse process of Modulation where the super imposed RF Wave and AF Wave are separated after it is received by a receiver antenna. The audio signal on being amplified and fed into a loud speaker (or headphone) reproduces the original speech or music. Now, this superimposing of input AF signal with RF Signal called as modulation is of two typesโฆ (i) Amplitude Modulation (AM)11: In amplitude modulation, the AF signal is superimposed on an RF carrier wave in such a manner that the frequency of the modulated wave is the same as that of the carrier wave, but its amplitude varies in accordance with the instantaneous amplitude of the modulating wave (message signal) (ii) Frequency Modulation (FM): In Frequency Modulation, the modulating wave is superimposed on a carrier wave in such a manner that the amplitude of the carrier wave remains constant, but its frequency varies in accordance with the instantaneous amplitude of the modulating wave. 8 FM stands for Frequency modulationโฆ We will see what that is shortly 9 The Modem in your computer is nothing but a Modulator โ Demodulator. 10 Remember that A Radio Frequency Wave is an Electromagnetic Wave that travels at the speed of light. 11 This is the AM and FM in your radio. 5 qed_amk_gesXII1011 AMPLITUDE MODULATION FRQUENCY MODULATION Audio Frequency Modulating Wave (Signal) Audio Frequency Modulating Wave (Signal) Radio Frequency Carrier Wave Radio Frequency Carrier Wave Amplitude Modulated Wave Frequency Modulated Wave The need for Modulationโฆ 1. There is a consequence of all this communication science that for efficient transmission and reception, the transmitting antenna should have a height roughly equal to a quarter of the wave length of the wave itself. Thus, for AF 10kHz (say), the required height of the antenna is about 7.5km! ๐ 1 ๐ 3 × 108 ๐/๐ = ( )= = 7500๐ = 7.5๐๐ (10 × 103 )๐ โ1 4 4 ๐ Now, if a carrier wave of frequency 1MHz is used, it turns out that the height of the tower needs to be only 75m which can be easily setup. 2. The energy carried by an audio (low frequency) signal is too small and so the power radiated from transmission is insignificant. The Power radiated from an antenna fed by a high frequency signal is quite large and the signal can therefore travel long distances. 3. All audio signals are of the range of 20Hz to 20,000kHz. Hence audio signals from different transmitting stations would overlap and cause confusion. The problem of overlapping of the signals from different transmitting stations is overcome by allotting a band of frequencies of the carrier wave to each station. 6 qed_amk_gesXII1011 CLASSIFICATION OF MAGNETIC MATERIALS In this section, I will tell you everything I know about magnetic classification of materials. That way, you will have the concepts very clear. However, you donโt have to study the whole thing as far as your exam is concerned. Check with the syllabus and learn what is required. Call me if you have doubts. As far as possible, I will try and indicate which is important and which is not! This may seem long, but a single reading will give you an idea as to what is happening... So it will be worth... Read it when you are taking a break... read it like a story. All substances show magnetic properties. Even materials that are not attracted by magnets show magnetic properties only they are so feeble that we cannot notice it. In order to understand how materials behave in the presence of an external magnetic field, you need to know three thingsโฆ 1. You already know that a current carrying loop is like a tiny bar magnet. If you have a current loop (of ANY shape), then the current either goes clockwise or counter clockwise and that loop will have an area. If the Area is treated as a vector here and the direction of the vector given by the right hand cork screw rule (We often did this in classโฆ rotate your right hand clockwise in the horizontal plane and then push it up). This will give you the direction of the Area Vector A. If the current flowing is โiโ, then the Magnetic Dipole Moment or the Magnetic Moment โµโ (your text book gives the variable The loop has current clockwise as seen from below โMโ for this) is given by the formula ๐ = ๐๐จ. If there are โNโ such loops (like in the case of a solenoid), then we have ๐ = ๐๐๐จ. This magnetic moment vector gives us the strength of the magnetic field. Higher the value of ๐ = ๐๐๐จ, stronger is the magnetic field in the vicinity. As the formula clearly indicates, the Magnetic Moment vector points in the direction of the Area Vector12. This Magnetic moment ๐ = ๐๐๐จ can be said to be like a tiny bar magnet as shown in the figure. The ๐ vector always points in the direction from South to North Pole of this Magnet as shown in the figure. So in short, a current loop can be considered as a tiny bar magnet and this loop for mathematical purposes can be represented by the Magnetic Dipole moment vector that points from South to North Pole of the equivalent bar magnet. Remember that the loop need not always be circular. It can be of any shape (rectangular, square or any irregular shape) as long as it will have a defined Area Vector! 2. When such a Magnetic Moment ๐ is brought in the presence of an external magnetic field B, the moment vector tries to align itself in the direction of the field as the north side of the magnetic moment (the arrow head of the vector) goes in the direction of the field and the south side of the magnetic moment (the tail of the vector) goes opposite to the direction of the external magnetic field B and how successful this aligning is depends on the strength of the field (See figure). This is just like how an electric dipole aligns itself in the presence of an external Electric field. The positive charge (the arrow head of the electric dipole moment vector) goes in the direction of the Electric field while at the same time the negative charge (the tail of the electric dipole moment vector) goes in the direction opposite to that of the field. 3. As you know, all materials are made up of atoms and molecules which are made up of electrons spinning about its own axis and revolving around the nucleus. Each such electron constitutes a tiny bar magnet (as it goes around, it constitute a current in a loop of very tiny area!). Or in other words, electrons contribute to a Magnetic dipole moment 12 This Magnetic Dipole Moment ๐ = ๐๐จ is analogous to the electric dipole moment that we defined as ๐ = 2๐๐ณ, where q is the charge and 2L is the vector distance between the two charges. Here, the vector p takes the direction of L. 7 qed_amk_gesXII1011 within the atom or the molecule. Therefore how materials behave in an external magnetic field will depend on the electronic configuration of these all these billions and billions of atoms and molecules that make up a material. We do not see the atoms and molecule; we only see the material and how it behaves. Now that you have an idea as to what a Magnetic dipole is, and how it behaves in the presence of an external magnetic field, and of how all substances are made of billions and billions of such very tiny bar magnets, we are ready to talk about how these materials behave in an external magnetic field. Depending on how materials behave in the presence of an external magnetic field, they are divided into three categories namely Diamagnetic, Paramagnetic and Ferromagnetic materials. We will discuss them qualitatively as well as quantitatively here. You also need to know that all materials have thermal energy and depending on the temperature of the substance, the amount of thermal energy will vary. Due to the thermal energy the atoms and molecules in the material are in very constant thermal agitation. More the temperature, more the thermal energy and hence more the thermal agitation of the atoms and molecules and electrons of the material. Therefore, when a material is subject to an external magnetic field B, how far the field will be successful in aligning the magnetic moment vectors (tiny bar magnets) of each of those atoms and molecules in the direction of the field will naturally depend on the temperature of the material and on the strength of the applied external field B itself. Sometimes, if the field is not strong enough, the thermal agitation will overcome the external Magnetic field. As you make the field stronger, the chances of success will increase. Diamagnetism In nature, we see that all materials, when you introduce them to an external magnetic field will to some degree oppose the field. All material will produce on an atomic scale an emf that opposes the applied external magnetic field. This is contrary to what we have discussed above but it is true. Why this is so can only be understood through the laws of Quantum Mechanics and hence we make no attempt to deal with it here but we will accept it13. As a result, what will happen is that the field inside the diamagnetic material is always a little smaller than that of the external field as the dipoles will oppose the external field. Examples of diamagnetic materials are Zinc, Copper, Silver, Gold, Lead, water, Mercury, Sodium Chloride, Nitrogen, Hydrogen etc. Paramagnetism There are many substances where the atoms and the molecules themselves have a magnetic dipole moments. So you can think of them as being little magnets. If you have no external magnetic field, then these dipoles are extremely chaotically oriented and so the total net magnetic field is zero and so they are not permanent magnets. But the moment you expose them to an external magnetic field, this magnetic field will try to align them and the degree of success will depend on the strength of the magnet field and the temperature. The lower the temperature, the easier it is. The tiny magnetic moments within the material will try and align itself to the external magnetic field as we have discussed in the previous page. As a result, what will happen is that the field inside the paramagnetic material is always a little higher than that of the external field as the dipoles will add on to the external field. The moment we remove the external field, all of the tiny bar magnets goes back to being chaotic and therefore there is no permanent magnetism left. In the presence of a non uniform magnetic field, the paramagnetic material will always attract to the stronger side of the field. Examples of paramagnetic substances are Aluminium, Sodium, Platinum, Manganese, Antimony, Copper Chloride, Liquid Oxygen, solution of salts of Iron, nickel etc. Ferromagnetism We have a third form know as ferromagnetism which is also the most interesting. There are substances that we know in nature that have just in the case of paramagnetic substances inherent permanent dipole moment. They also have a net zero magnetic moment (means they are not permanent magnets). But however, unlike in the case of paramagnetic substances, within the materials, there are small spaces or domains within the material of the order of 0.1 mm to 0.3mm where the dipoles are 100% aligned in certain given directions14. So within a certain small area (domain), the magnetic moment is 13 You may say Lenz Law is the reason (faradays law of electromagnetic induction)โฆ WRONG! It has nothing to do with Lenz law; Lenz law is the production of opposing emf by the free electrons in a conductor in the presence of a changing magnetic field. This is a permanent external magnetic field that we are talking about. 14 The reasons for this can only be understood using Quantum Mechanics 8 qed_amk_gesXII1011 non zero, meaning that they are permanent magnets within that area only. Now if you move to another nearby domain, it will have a different orientation but will have 100% orientation in that direction. Like this the entire material is made of large number of domains consisting of 1017 to 1021 atoms that are permanent magnets but the material as a whole may not be magnetic. Now if the material is exposed to an external magnetic field, the domains as a whole will try to align itself to the external field and the degree of success will depend on the strength of the field and the temperature; lower the temperature, the lower the thermal agitation and then the easier it is to orient these domains. As a result, what will happen is that the field inside the ferromagnetic material can be up to thousands of times higher than that of the external field as the dipoles will aid the external field. A diagrammatic representation of these domains before and after the introduction of an external magnetic field is given in the diagrams above (In the second diagram the field is applied from below to above as can be seen). Now unlike in the case of paramagnetic substances, once the external field in introduced and then removed, some of the domains may continue to remain aligned in the direction in which the field was applied. If we very carefully remove the external field, undoubtedly some of the domains will flip back to its original configuration because of thermal agitation while some will remain oriented in the direction the field was applied and thereby giving the material a net magnetic moment and hence it acts like a magnet (we know from daily experience that that when paper clips are attached to a magnet for a long time, even after the magnetic is removed, it continues to attract other paperclips. Thatโs the idea!!!). In order to lose this permanent magnetism, we can either hit the material hard on some object or with some object or heat it! When this is done, we distort the orientation and force it to come back to how it was originally and hence it loses its magnetism! In the presence of a non uniform magnetic field, like in the case of the paramagnetic material, the ferromagnetic material will also always attract itself to the stronger side of the field only in this case the attraction is thousands of times stronger. This is why a paper clip will attract itself to the North Pole or the South Pole of a magnet, depending on which one is closer to it. Examples of Ferromagnetic materials are Iron, Cobalt, Nickel, Magnetite etc. In most cases, it is almost impossible to get paramagnetic materials to attract on a magnet as the force of attraction is only 3% to 5% of the weight of the material itself. This is also the reason why we see an iron rod (ferromagnetic) attracting a magnet while an Aluminium rod (paramagnetic) does not. Even though there is attraction, it is very feeble and cannot be noticed under ordinary conditions. So in a way, the difference between Paramagnetism and Ferromagnetism is only that of intensity. A 15kg of Iron will attract to a magnet while even a few hundred grams of Aluminium will not as Ferromagnetic materials are far more intense than Paramagnetic materials. Here are a few definitions you need to know for the sake of exam... (a) Magnetic Induction (B): When a piece of any substance is place in an external Magnetic field, the substance becomes magnetised and this phenomenon is called Magnetic induction (B). It has a unit Tesla (T) (b) Intensity of Magnetisation (I): The Intensity, or simple the magnetisation of a magnetised substance represents the extend to which the substance is magnetised. It is defined as the magnetic Moment per unit volume of the magnetised substance and is denoted by I. Numerically, ๐ฐ = ๐/๐ where V is the volume and ๐ is the Magnetic Moment. It has a unit of A/m (c) Magnetic Intensity or Magnetic Field Strength (H): When a substance is place in an external Magnetic field, it becomes magnetised. The actual magnetic field inside the substance is the sum of the external magnetic field and the field due to its magnetisation. The capability of the magnetising field to magnetise the substance is expressed by means of a vector H, called the Magnetic Intensity of the Field. The magnetic intensity is define through the vector relation 9 qed_amk_gesXII1011 ๐ โ๐ ฮผ0 Where ๐0 is the permeability of free space. From a practical point of view, H is very important, especially in the case of ferromagnetic materials, as it can be controlled by adjusting the current, say in coils or solenoids. Its unit is the same as that of I A/m ๐= (d) Magnetic Permeability (µ): It is the measure of conduction of Magnetic field lines through it. It is defines as the ratio of Magnetic Induction B inside the magnetised substance to the Magnetic Intensity H of the magnetising field. ๐ ฮผ= ๐ (e) Relative Permeability (µr or ฮบm): It is the ratio of magnetic permeability of the substance to the permeability of free space. It is a dimensionless quantity, just a number. ๐ ๐๐ = ๐0 (f) Magnetic Susceptibility (๐๐ ): It is a measure of how easily a substance is magnetised in a magnetising field. It may be define as the ratio of the intensity of magnetisation to the magnetic intensity of the magnetising field that is, ๐ฐ ๐๐ = ๐ฏ We have seen that for all materials dia, para or ferromagnetic, the field inside the material is different from what the field would be without external field. In Many cases, the field inside (B according to our definitions above) is proportional to the External Field (Bo). So we can write that ๐ฉ โ ๐ฉ๐ โน ๐ฉ = ฮผr ๐ฉ๐ So now if we look at the values of ฮผr , we can easily see the difference between dia, para and ferromagnetic materials. We know that just as in the case of relative permittivity, the value of relative permeability must also be always greater than one. However, in the case of diamagnetic materials, it is very slightly lesser than one. So if we now plug that value into the equation ๐ฉ = ฮผr ๐ฉ๐, we clearly see that the value of field inside the material (B) is smaller than the value of the external field (Bo) showing that it opposes the external magnetic field. On the other hand, the value of ฮผr for para magnetic material is slightly greater that 1 and so we see that in the relation ๐ฉ = ฮผr ๐ฉ๐, the value of B is slightly greater than the value of the external field (B). Finally for ferromagnetic material, the value of ฮผr is very large indicating that the field inside is much, much greater that the field outside. Now, since the value of relative permeability for dia and para are very close to 1, it is convenient to express it as ฮผr = 1 + ๐๐ And therefore, the value of Magnetic Susceptibility ( ๐๐ ) also can decides whether a substance is dia, para or ferromagnetic in nature. The table below will give you a feel for the numbers. This is NOT for you to study! Diamagnetic materials ฮผr < 1 ๐๐ ๐๐ < 0 Diamagnetic Material Bismuth Copper Water Nitrogen (1 atm) Paramagnetic materials ฮผr > 1 ๐๐ ๐๐ > 0 ๐๐ Paramagnetic Material ๐๐ Aluminium (300K) Oxygen (1 atm, 300K) Liquid Oxygen (90K) +2.0 × 10โ5 +2.0 × 10โ6 +3.5 × 10โ3 โ4 โ1.7 × 10 โ1.0 × 10โ5 โ1.0 × 10โ5 โ7.0 × 10โ9 Ferromagnetic materials ฮผr โซ 1 or ๐๐ โซ 0 ฮผr โ ๐๐ โ 105 โผ! As we have seen that the magnetic property of a substance is Temperature dependant, we have an interesting phenomenon in nature. There is a very specific temperature for every substance above which the ferromagnetic substance suddenly turns paramagnetic in nature. This temperature is called the Curie temperature. This phenomenon was discovered by Curie in 1895. It turns out that the Curie temperature has a dependence on the magnetic susceptibility (ฯm ) of the substance as follows... 1 ฯm โ TC 10 qed_amk_gesXII1011 Where TC is the curie temperature. Iron for instance has a curie temperature of only 770 ºC. Hence, it can be shown experimentally that iron stick to a magnet. But if we were to heat it, then suddenly, it will lose its magnetic force and fall off. When it cools, it will attract again! GRATING (comes under the chapter of diffraction) Those of you who wear spectacles (especially plastic lens) would have noticed that when they are scratched (because you rub it too much with rough cloth or with your hands), it is difficult to see in the night because all sources of light seem to spread out the light irregularly instead of coming regularly to your eye. This happens because the scratch forms a small potion on the lens that is opaque to light and light diffracts around the edges of it. The idea of a diffraction grating is just that. Take a nice, fine piece of rectangular glass plate and scratch vertical lines on it. How many lines? Of the order of 6000 lines in just 1 cm! Now why is this done? Since light diffract around the opaque edges the light spreads out and here since all the lines are made in a very orderly manner and vertical, the spreading of light is very regular (unlike in the case of your spectacles where the scratches are very disorderly). Now we also know that the spreading is a property of the wave length of the light used and so this can be used to study various optical phenomena. If each of these โscratchesโ (the opaque region) have a thickness of โdโ and each transparent region have a thickness โeโ. Since they are regularly made, every opaque region will be followed by a transparent region, then an opaque region, then a transparent region and so on in a very regular repetitive manner. From the diagram, remembering the derivations for diffraction, we see that the path difference at a certain angular dispersion ๐ is given by the formula ๐2 ๐พ = ๐1 ๐2 sin ๐ = (๐ + ๐) sin ๐. The two wavelets from S1 and S2 will reinforce each other when brought to a focus P by a lens, if the path difference equals a whole number multiple of the wave length (๐). Thus for reinforcement we have (๐ + ๐) sin ๐ = ๐๐ Here โmโ is called the order of the spectrum. What does this mean? If we use mercury vapour lamp and pass the light through a prism using a spectrometer, you will see the spectrum in the telescope. This you have already seen in the lab. It turns out that if you use a grating instead of a prism, you will get to see just the same thing in the same way but with one difference. There will be more than one set of thee spectra and they are much fainter and they will be symmetrically arranged on either side of the incident ray. The one that comes first on either side is called the โfirst order spectrumโ for which we use the value ๐ = 1. If you turn the spectrometer further away from the incident ray, you will get another set of the same spectrum which is much fainter. This is seem on either side and will be the โsecond order spectrumโ ๐ = 2. So in short, it turns out that the grating is sort of a substitute for a prism but the principle behind the formation of the spectra is dispersion in the prism and diffraction in the case of the grating. If there are N number of lines per cm, then ๐(๐ + ๐) = 1๐๐ or, 1 ๐= ๐+๐ Therefore, we have the relation, ๐๐ sin ๐ = = ๐๐๐ (๐ + ๐) sin ๐ = ๐๐๐ This is the equation for the grating that is used in the lab. If we use a monochromatic light of wavelength ๐ and if the grating has N lines per cm and if we are looking at the first order grating where ๐ = 1, then the angular dispersion that can be seen through a spectrometer will be ๐ = sinโ1 (๐๐๐). So calculating the angle at which say red light is seen and knowing the value of m and N, we can calculate the wavelength of red light! 11 qed_amk_gesXII1011