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Electromagnetism & Its Applications 1 Electricity and Magnetism • An electricity can be converted to be a magnetism or vice versa. – With electricity, it turned out to be useful to define an electric field rather than always working in terms of electric forces. Electricity Magnetism 2 Magnetic Field • Magnetic fields are produced by electric currents, which can be – macroscopic currents in wires, or – microscopic currents associated with electrons in atomic orbits. • The magnetic field B is defined in terms of force on moving charge in the Lorentz force law. F qv xB • Magnetic field sources are essentially dipole in nature, having a north and south magnetic pole. 3 Biot-Savart Formula Magnetic field at P, produced by dl, is given by: i dl sin dB k 2 r Current (i) dl α r dB P R 4 Magnetic Field Sources 5 Magnetic Field of Current • The magnetic field lines around a long wire which carries an electric current form concentric circles around the wire. • The direction of the magnetic field is perpendicular to the wire and is in the direction the fingers of your right hand would curl if you wrapped them around the wire with your thumb in the direction of the current. The constant 0 is the permeability of free space. 6 Magnetic Field of Current Loop • Electric current in a circular loop creates a magnetic field which is more concentrated in the center of the loop than outside the loop. • Examining the direction of the magnetic field produced by a current-carrying segment of wire shows that all parts of the loop contribute magnetic field in the same direction inside the loop. Stacking multiple loops concentrates the field even more into what is called a solenoid. 7 Field at Center of Current Loop • The form of the magnetic field from a current element in the Biot-Savart law becomes • which in this case simplifies greatly because the angle =90 ° for all points along the path and the distance to the field point is constant. The integral becomes 8 Field on Axis of Current Loop • The application of the Biot-Savart law on the centerline of a current loop involves integrating the z-component. • The symmetry is such that all the terms in this element are constant except the dL , which when integrated just gives the circumference of the circle. The magnetic field is then 9 Field on Axis of Current Loop … 10 Solenoid • A long straight coil of wire can be used to generate a nearly uniform magnetic field similar to that of a bar magnet. • Such coils, called solenoids, have an enormous number of practical applications. • The field can be greatly strengthened by the addition of an iron core. Such cores are typical in electromagnets. 11 Solenoid Field from Ampere's Law • Taking a rectangular path about which to evaluate Ampere's Law such that the length of the side parallel to the solenoid field is L gives a contribution BL inside the coil. – The field is essentially perpendicular to the sides of the path, giving negligible contribution. – If the end is taken so far from the coil that the field is negligible, then the length inside the coil is the dominant contribution. • This admittedly idealized case for Ampere's Law gives • This turns out to be a good approximation for the solenoid field, particularly in the case of an iron core solenoid. 12 Solenoid Magnetic Field Calculation • At the center of a long solenoid – Active formula: click on the quantity you wish to calculate. Magnetic field = permeability x turn density x current 13 Bar Magnet • The lines of magnetic field from a bar magnet form closed lines. • By convention, the field direction is taken to be outward from the North pole and in to the South pole of the magnet. • Permanent magnets can be made from ferromagnetic materials. 14 Electric and Magnetic Sources • The electric field of a point charge is radially outward from a positive charge. – Electric sources are inherently "monopole" or point charge sources. • The magnetic field of a bar magnet. – Magnetic sources are inherently dipole sources - you can't isolate North or South "monopoles". 15 Bar Magnet and Solenoid • The magnetic field produced by electric current in a solenoid coil is similar to that of a bar magnet. 16 Iron Core Solenoid • Electromagnets are usually in the form of iron core solenoids. The ferromagnetic property of the iron core causes the internal magnetic domains of the iron to line up with the smaller driving magnetic field produced by the current in the solenoid. – The effect is the multiplication of the magnetic field by factors of tens to even thousands. The solenoid field relationship is – and k is the relative permeability of the iron, shows the magnifying effect of the iron core. 17 Magnetic Field of the Earth • The earth's magnetic field is similar to that of a bar magnet tilted 11 degrees from the spin axis of the earth. • The problem with that picture is that the Curie temperature of iron is about 770 C . • The earth's core is hotter than that and therefore not magnetic. So how did the earth get its magnetic field? • The earth's magnetic field is attributed to a dynamo effect of circulating electric current, but it is not constant in direction. – Rock specimens of different age in similar locations have different directions of permanent magnetization. Evidence for 171 magnetic field reversals during the past 71 million years has been reported. 18 Electric Motors • Electric motors involve rotating coils of wire which are driven by the magnetic force exerted by a magnetic field on an electric current. • They transform electrical energy into mechanical energy. 19 How Does an Electric Motor Work? 20 DC Motor Operation 21 DC Motor Operation: electric current 22 DC Motor Operation: magnetic field 23 DC Motor Operation: magnetic force 24 Tape Recording Process 25 Tape Head Action • An electric current in a coil of wire produces a magnetic field similar to that of a bar magnet, and that field is much stronger if the coil has a ferromagnetic (iron-like) core. • Tape heads are made from rings of ferromagnetic material with a gap where the tape contacts it so the magnetic field can fringe out to magnetize the tape. – A coil of wire around the ring carries the current to produce a magnetic field proportional to the signal to be recorded. – If an already magnetized tape is passed beneath the head, it can induce a voltage in the coil. – Thus the same head can be used for recording and playback. 26 Cassette Tape Head Arrangement • The basic tape head action involves an oscillating current in a coil. – The magnetic field produced in a ring of ferromagnetic material fringes out to the tape material at the gap. – For stereo cassette tape heads, there are two such mechanisms to record and playback from parallel tracks on the tape. 27 Magnetic Emulsions • The recording medium for the tape recording process is typically made by embedding tiny magnetic oxide particles in a plastic binder on a polyester film tape. – Iron oxide has been the most widely used oxide, but chromium oxide and metal particles provide a better signal-to-noise ratio and a wider dynamic range. – The oxide particles are on the order of 0.5 micrometers in size and the polyester tape backing may be as thin as 0.5 mil (.01 mm). – The oxide particles themselves do not move during recording. – Rather their magnetic domains are reoriented by the magnetic field from the tape head. 28 Erase Head • Before passing over the record head, a tape in a recorder passes over the erase head which applies a high amplitude, high frequency AC magnetic field to the tape to erase any previously recorded signal and to thoroughly randomize the magnetization of the magnetic emulsion. – Typically, the tape passes over the erase head immediately before passing over the record head. • The gap in the erase head is wider than those in the record head; the tape stays in the field of the head longer to thoroughly erase any previously recorded signal. 29 Biasing • High fidelity tape recording requires a high frequency biasing signal to be applied to the tape head along with the signal to "stir" the magnetization of the tape and make sure each part of the signal has the same magnetic starting conditions for recording. – This is because magnetic tapes are very sensitive to their previous magnetic history, a property called hysteresis. • A magnetic "image" of a sound signal can be stored on tape in the form of magnetized iron oxide or chromium dioxide granules in a magnetic emulsion. – The tiny granules are fixed on a polyester film base, but the direction and extent of their magnetization can be changed to record an input signal from a tape head 30 Tape Playback • When a magnetized tape passes under the playback head of a tape recorder, the ferromagnetic material in the tape head is magnetized and that magnetic field penetrates a coil of wire which is wrapped around it. – Any change in magnetic field induces a voltage in the coil according to Faraday's law. – This induced voltage forms an electrical image of the signal which is recorded on the tape. • Problem: The magnetization of the magnetic emulsion is proportional to the recorded signal while the induced voltage in the coil is proportional to the rate at which the magnetization in the coil changes. – This means that for a signal with twice the frequency, the output signal is twice as great for the same degree of magnetization of the tape. – It is therefore necessary to compensate for this increase in signal to keep high frequencies from being boosted by a factor of two for each octave increase in pitch. – This compensation process is called equalization. 31 Biasing in Tape Recording • A music signal alone cannot be used to produce a faithful tape recording of a sound because the magnetization of the tape is so sensitive to its previous magnetic history, even the effects of the signal recorded just ahead of it. • A high frequency bias signal is typically applied to the tape through the tape head along with the music signal to remove the effects of this magnetic history. • This large bias signal (typically 40 to 150 kHz in frequency) keeps "stirring" the magnetization so that each signal to be recorded encounters the same magnetic starting conditions. • The necessity for biasing has its origin in the magnetic property called hysteresis - the magnetic material tends to hold onto any magnetization it receives and must be actively driven back to zero to start over. • Magnetic emulsions made with chromium dioxide require a larger biasing signal to make use of their wider dynamic range, so modern recorders have different bias settings for iron oxide, chromium dioxide, and metal tapes. • With optimum biasing, the recorded magnetic image is proportional to the signal current applied to the record head. 32 Bias During Recording • To record a sine wave on tape, you mix it with a high frequency bias signal. – The bias keeps the magnetic domains "stirred", with an average magnetization in the direction of the signal voltage you wish to record. – As the head passes, a net magnetization proportional to the sine wave signal remains. 33 Optimum Biasing 34 Hysteresis in Magnetic Recording • Because of hysteresis, an input signal at the level indicated by the dashed line could give a magnetization anywhere between C and D, depending upon the immediate previous history of the tape (i.e., the signal which preceded it). – This clearly unacceptable situation is remedied by the bias current which cycles the oxide grains around their hysteresis loops so quickly that the magetization averages to zero when no signal is applied. The result of the bias signal is like a magnetic eddy which settles down to zero if there is no signal superimposed upon it. If there is a signal, it offsets the bias signal so that it leaves a remnant magnetization proportional to the signal offset. 35 Hysteresis in Magnetic Recording 36 Dynamic Loudspeaker Principle • A current-carrying wire in a magnetic field experiences a magnetic force perpendicular to the wire. 37 Loudspeaker Details • A light voice coil is mounted so that it can move freely inside the magnetic field of a strong permanent magnet. • The speaker cone is attached to the voice coil and attached with a flexible mounting to the outer ring of the speaker support. – Because there is a definite "home" or equilibrium position for the speaker cone and there is elasticity of the mounting structure, there is inevitably a free cone resonant frequency like that of a mass on a spring. – The frequency can be determined by adjusting the mass and stiffness of the cone and voice coil, and it can be damped and broadened by the nature of the construction, but that natural mechanical frequency of vibration is always there and enhances the frequencies in the frequency range near resonance. – Part of the role of a good enclosure is to minimize the impact of this resonant frequency. 38 Types of Enclosures • The production of a good high-fidelity loudspeaker requires that the speakers be enclosed because of a number of basic properties of loudspeakers. • Just putting a single dynamic loudspeaker in a closed box will improve its sound quality dramatically. • Modern loudspeaker enclosures typically involve multiple loudspeakers with a crossover network to provide a more nearly uniform frequency response across the audio frequency range. • Other techniques such as those used in bass reflex enclosures may be used to extend the useful bass range of the loudspeakers. 39 Use of Multiple Drivers in Loudspeakers • Even with a good enclosure, a single loudspeaker cannot be expected to deliver optimally balanced sound over the full audible sound spectrum. – For the production of high frequencies, the driving element should be small and light to be able to respond rapidly to the applied signal. Such high frequency speakers are called "tweeters". – On the other hand, a bass speaker should be large to efficiently impedance match to the air. Such speakers, called "woofers", must also be supplied with more power since the signal must drive a larger mass. 40 Hard disk • A hard disk drive (HDD, or also hard drive or the now-obsolete usage hard file) is a non-volatile data storage device that stores data on a magnetic surface layered onto hard disk platters. 41 Hard disk • A hard disk uses rotating platters (disks). – Each platter has a smooth magnetic surface on which digital data is stored. Information is written to the disk by applying a magnetic field from a read-write head that flies very close over the magnetic surface. – The magnetic medium (film) on the disk surface changes its magnetization in microscopic spots (bits) due to the head's write field. – The information can be read back by a magnetoresistive (MR) read sensor which is part of the same head structure on the trailing end of the flying slider. – The read sensor detects the magnetic flux emanating from the bit transitions passing underneath it through a small change of the MR sensor's electric resistance. 42 Hard disk • Due to the extremely close spacing between the heads and the disk surface, any contamination of the read-write heads or disk platters can lead to a head crash — a failure of the disk in which the head scrapes across the platter surface, often grinding away the thin magnetic film. • For Giant Magnetoresistive (GMR) heads in particular, a minor head crash from contamination (that does not remove the magnetic surface of the disk) will still result in the head temporarily overheating, due to friction with the disk surface, and can render the data unreadable for a short period until the head temperature stabilizes (so called "thermal asperity," a problem which can partially be dealt with proper electronic filtering of the read signal). 43 Hard disk • Using rigid platters and sealing the unit allows much tighter tolerances than in a floppy disk. • Consequently, hard disks can store much more data than floppy disk and access and transmit it faster. • In 2005, a typical workstation hard disk might store between 80 GB and 500 GB of data, rotate at 7,200 to 10,000 rpm, and have a sequential media transfer rate of over 50 MB/s. • The fastest workstation and server hard drives spin at 15,000 rpm, and can achieve sequential media transfer speeds up to and beyond 80 MB/s. • Notebook hard drives, which are physically smaller than their desktop counterparts, tend to be slower and have less capacity. • Most spin at only 4,200 rpm or 5,400 rpm, whereas the newest top models spin at 7,200 rpm. 44 Hard disk • The platters are made from a non-magnetic material, usually glass or aluminum, and coated on both sides with a thin layer of magnetic material. – Older drives used iron(III) oxide, but current drives use a thin film of a cobaltbased alloy, applied by sputtering. • The magnetic surface in the hard drive is divided into small sub-micrometresized magnetic regions, each of which is used to represent a single binary unit of information. – Each of these magnetic regions is further subdivided into a few hundred magnetic grains. Each grain is considered to be a single magnetic domain. – Each grain will thus be a magnetic dipole which points in a certain direction, creating a magnetic field around it. – All of the grains in a magnetic region are expected to point in the same direction, so that the magnetic region as a whole also has a magnetic dipole moment and an associated magnetic field. 45 Hard disk • The data is encoded through the change in magnetization at a region boundary, rather than the direction of magnetization of a region. – If the magnetization reverses between two magnetic domains, this signifies one state, while no change in magnetization signifies the other state. – For various reasons, the actual binary data is encoded using consecutive sequences of these two possible states, rather than the states themselves. – Most hard drives use a form of Run Length Limited coding, for example. – At a boundary where the magnetization reverses, magnetic field lines will be dense and perpendicular to the medium. – The read head is designed to detect these changes. 46 Hard disk • In older hard drives, the read head was usually a small inductor, often filled with a paramagnetic material in order to enhance the signal. – As it passes over a boundary with a magnetization reversal, the read head experiences magnetic flux, which is converted by the inductor into an electric current. • Modern hard drives usually have a read head that makes use of the Giant Magnetoresistive effect, which causes the resistance of certain materials to change in response to a strong magnetic field. – As this type of read head passes over a boundary with a magnetization reversal, the strong magnetic field will cause its resistance to change in a detectable way. 47 Hard disk • The magnetic surface and how it operates. In this case the binary data encoded using frequency modulation 48 Hard disk • Comparison of the transition width caused by Neel Spikes in continuous media and granular media, at a boundary between two magnetic regions of opposite magnetization 49 Credit Cards • The phone companies, gas companies and department stores have their own numbering systems, ANSI Standard X4.131983 is the system used by most national credit-card systems 50 Credit Cards • The stripe on the back of a credit card is a magnetic stripe, often called a magstripe. – The magstripe is made up of tiny iron-based magnetic particles in a plasticlike film. Each particle is really a tiny bar magnet about 20-millionths of an inch long. • The magstripe can be "written" because the tiny bar magnets can be magnetized in either a north or south pole direction. – The magstripe on the back of the card is very similar to a piece of cassette tape • A magstripe reader can understand the information on the three-track stripe. • If the ATM isn't accepting your card, your problem is probably either: – A dirty or scratched magstripe – An erased magstripe (The most common causes for erased magstripes are exposure to magnets, like the small ones used to hold notes and pictures on the refrigerator, and exposure to a store's electronic article surveillance (EAS) tag demagnetizer.) 51