Chapter 23: Electromagnetic Induction, Transformers PDF

CHAPTER 23: ELECTRO MAGNETIC INDUCTION, Transformers MRS. POOJA BRAHMAIAHCHARI Introduction Specifically, we know that a current creates a magnetic field. If nature is symmetric here, then perhaps a magnetic field can create a current. The Hall effect is a voltage caused by a m...

CHAPTER 23: ELECTRO MAGNETIC INDUCTION, Transformers MRS. POOJA BRAHMAIAHCHARI Introduction Specifically, we know that a current creates a magnetic field. If nature is symmetric here, then perhaps a magnetic field can create a current. The Hall effect is a voltage caused by a magnetic force. That voltage could drive a current. Can magnetic fields cause currents? The English scientist Michael Faraday (1791–1862) and the American scientist Joseph Henry (1797–1878) independently demonstrated that magnetic fields can produce currents. The basic process of generating emfs (electromotive force) and, hence, currents with magnetic fields is known as induction; this process is also called magnetic induction to distinguish it from charging by induction, which utilizes the Coulomb force. Induced Emf and Magnetic Flux The apparatus used by Faraday to demonstrate that magnetic fields can create currents is illustrated in Figure. When the switch is closed, a magnetic field is produced in the coil on the top part of the iron ring and transmitted to the coil on the bottom part of the ring.  The galvanometer is used to detect any current induced in the coil on the bottom. It was found that each time the switch is closed, the galvanometer detects a current in one direction in the coil on the bottom. Each time the switch is opened, the galvanometer detects a current in the opposite direction. Interestingly, if the switch remains closed or open for any length of time, there is no current through the galvanometer. Closing and opening the switch induces the current. It is the change in magnetic field that creates the current. More basic than the current that flows is the emf that causes it. The current is a result of an emf induced by a changing magnetic field, whether or not there is a path for current to flow. All this says is that a change in magnetic field causes a current  An emf is induced in the coil when a bar magnet is pushed in and out of it. Emfs of opposite signs are produced by motion in opposite directions, and the emfs are also reversed by reversing poles. The same emfs are produced if the coil is moved relative to the magnet. The greater the speed, the greater the magnitude of the emf, and the emf is zero when there is no motion.  The method of inducing an emf used in most electric generators is shown in Figure. It is alternating because it goes to zero occasionally A coil is rotated in a magnetic field, producing an alternating current emf, which depends on rotation rate and other factors. So, we see that changing the magnitude or direction of a magnetic field produces an emf. Experiments revealed that there is a crucial quantity called the magnetic flux,𝜱, given by Φ = 𝐵𝐴 cos 𝜃 where B is the magnetic field strength over an area A , at an angle θ with the perpendicular to the area as shown in figure.  Any change in magnetic flux induces an emf. This process is defined to be electromagnetic induction. Units of magnetic flux Φ are Weber or T. m2. 𝐵 cos θ = 𝐵⏊ which is the component of B perpendicular to the area. Thus, magnetic flux is , Φ = 𝐵⏊ 𝐴, the product of the area and the component of the magnetic field perpendicular to it. This is just saying that the angle you use for Cos0 is the angle angle between the perpendicular to the surface and the magnetic field Faraday’s Law of Induction: Lenz’s Law Faraday’s experiments showed that the emf induced by a change in magnetic flux depends on only a few factors. First, emf is directly proportional to the change in flux ∆Ф. Second, emf is greatest when the change in time ∆t is smallest—that is, emf is inversely proportional to ∆t. Finally, if a coil has N turns, an emf will be produced that is N times greater than for a single coil, so that emf is directly proportional to N. The equation for the emf induced by a change in magnetic flux is ΔΦ 𝑒𝑚𝑓 = −𝑁 Δ𝑡 This relationship is known as Faraday’s law of induction. The units for emf are volts, as is usual. The more turns of the coil, the greater the flux and the smaller the time the greater the emf produced  The minus sign in Faraday’s law of induction is very important. The minus means that the emf creates a current I and magnetic field B that oppose the change in flux ∆Ф —this is known as Lenz’s law. The direction (given by the minus sign) of the emf is so important that it is called Lenz’s law after the Russian Heinrich Lenz (1804–1865), who, like Faraday and Henry, independently investigated aspects of induction. The whole idea of lenzs law is that when you have a magnet and you push it against a wire that changes the flux, this then creates an indued current in the wire. Lenz law states that the current created must oppose the force that created it. In the exmaples of magnets all this is saying is that the magnet will create a current and that current will go in the direction so that it creates a magnetic field that opposes the magnet that created the current in the first place. If this wasnt the case the magnetic fields would continue adding additively and violate the law of conservation of energy. (a) When this bar magnet is thrust into the coil, the strength of the magnetic field increases in the coil. The current induced in the coil creates another field, in the opposite direction of the bar magnet’s to oppose the increase. This is one aspect of Lenz’s law—induction opposes any change in flux. (b) and (c) are two other situations. The direction of the induced Bcoil shown indeed opposes the change in flux and that the current direction shown is consistent with RHR-2. 1. A single circular loop of wire(r = 25cm) is perpendicular to a magnetic field which increases from 1.5 T to 4.8T in 23ms. a) Calculate the change in magnetic flux. b) What is the induced emf? c) Calculate the induced current in wire if total resistance is 20 ohms. a) Change in flux = BA cos b) c) Change in flux = (4.8-1.5) (0.196) Change in flux = 0.65 Weber I = V/R Emf = change in flux / time I=28.3/20 Emf = 28.3 V I = 1.4 A 2. A flexible rectangular coil of wire 150 loops is stretched in such a way that its dimension changes from 5cm x 8cm to 7cm x 11cm in 0.15s in magnetic field of 25T that is 35o relative to plane of coil. Calculate induced emf. Important to note that the angle you use is the Change in flux = BA cos theta angle relative to the perpendicular NOT the Change in flux = 25 ( 7.7x10^-3 - 4x10 ^-3) cos 55 angle to the plane so you have to do 90 - 35 to Change in flux = 0.053 weber find the angle Emf = N x (change in flux/ time) Emf = 150 x ( 0.053 x 0.15) emf = 53 V Applications of Electromagnetic Induction A very important application has to do with audio and video recording tapes. A signal in the form of a varying input current from a microphone or camera goes to the recording head. These signals produce varying magnetic fields at the recording head. Similar principles apply to computer hard drives, except at a much faster rate. Today, most hard drive readout devices do not work on the principle of induction, but use a technique known as giant magnetoresistance.  Another application of induction is found on the magnetic stripe on the back of your personal credit card as used at the grocery store or the ATM machine. Another application of electromagnetic induction is when electrical signals need to be transmitted across a barrier. Consider the cochlear implant shown in picture. Sound is picked up by a microphone on the outside of the skull and is used to set up a varying magnetic field. A current is induced in a receiver secured in the bone beneath the skin and transmitted to electrodes in the inner ear. Electromagnetic induction can be used in other instances where electric signals need to be conveyed across various media.  Another contemporary area of research in which electromagnetic induction is being successfully implement is transcranial magnetic simulation. A host of disorders, including depression and hallucinations can be traced to irregular localized electrical activity in the brain. Sleep apnea (“the cessation of breath”) affects both adults and infants (especially premature babies and it may be a cause of sudden infant deaths). In such individuals, breath can stop repeatedly during their sleep. A cessation of more than 20 seconds can be very dangerous. Stroke, heart failure, and tiredness are just some of the possible consequences for a person having sleep apnea. The concern in infants is the stopping of breath for these longer times.  One type of monitor to alert parents when a child is not breathing uses electromagnetic induction. A wire wrapped around the infant’s chest has an alternating current running through it. The expansion and contraction of the infant’s chest as the infant breathes changes the area through the coil. A pickup coil located nearby has an alternating current induced in it due to the changing magnetic field of the initial wire. If the child stops breathing, there will be a change in the induced current, and so a parent can be alerted. Motional Emf Any change in magnetic flux induces an emf opposing that change—a process known as induction. Motion is one of the major causes of induction. For example, a magnet moved toward a coil induces an emf, and a coil moved toward a magnet produces a similar emf. In this section, we concentrate on motion in a magnetic field that is stationary relative to the Earth, producing what is loosely called motional emf. One situation where motional emf occurs is known as the Hall effect.  Charges moving in a magnetic field experience magnetic force 𝐹 = 𝑞𝑣𝐵 sin 𝜃, which moves opposite charges in opposite directions and produces an 𝑒𝑚𝑓 = 𝐵𝑙𝑣. (a) A motional is induced between the rails when this rod moves to the right in the uniform magnetic field. The magnetic field is into the page, perpendicular to the moving rod and rails and, hence, to the area enclosed by them. The reason the current goes that way is because it has to create a magnetic field that opposes the magnetic field that produced it. Do RHR-2 to determine what direction the current must flow so that the create B opposes the existing B  (b) Lenz’s law gives the directions of the induced field and current, and the polarity of the induced emf. Since the flux is increasing, the induced field is in the opposite direction, or out of the page. RHR-2 gives the current direction shown, and the polarity of the rod will drive such a current. RHR-1 also indicates the same polarity for the rod. The motional emf is given by the equation 𝑒𝑚𝑓 = 𝐵𝑙𝑣 (B, l and v are perpendicular) This is the same expression given for hall effect. Motional emf also occurs if the magnetic field moves and the rod (or other object) is stationary relative to the Earth. Eddy Currents and Magnetic Damping Motional emf is induced when a conductor moves in a magnetic field or when a magnetic field moves relative to a conductor. If motional emf can cause a current loop in the conductor, we refer to that current as an eddy current. Eddy currents can produce significant drag, called magnetic damping, on the motion involved.  Consider the figure shown in the previous slide, which swings a pendulum bob between the poles of a strong magnet. If the bob is metal, there is significant drag on the bob as it enters and leaves the field, quickly damping the motion. If, however, the bob is a slotted metal plate, as shown (b), there is a much smaller effect due to the magnet. (c) There is also no magnetic damping on a nonconducting bob, since the eddy currents are extremely small. Essentially the eddy current is produced in such a way so that the magnetic field that it produces will oppose the applied magnetic field. This slows down the piece of metal travelling through the magnet. As the flux is increasing, the eddy current will go upwards which will create a magnetic (counter clock wise) field that repels opposes its motion. As the flux is decreasing it creates an eddy current which creates a magnetic field that is clockwise and opposes the its motion.  As it enters from the left, flux increases, and so an eddy current is set up (Faraday’s law) in the counterclockwise direction (Lenz’s law), as shown. Only the right-hand side of the current loop is in the field, so that there is an unopposed force on it to the left (RHR-1). When the metal plate is completely inside the field, there is no eddy current if the field is uniform, since the flux remains constant in this region. But when the plate leaves the field on the right, flux decreases, causing an eddy current in the clockwise direction that, again, experiences a force to the left, further slowing the motion. Applications of Magnetic Damping One use of magnetic damping is found in sensitive laboratory balances. To have maximum sensitivity and accuracy, the balance must be as friction-free as possible. But if it is friction-free, then it will oscillate for a very long time. Magnetic damping is a simple and ideal solution. With magnetic damping, drag is proportional to speed and becomes zero at zero velocity. Thus, the oscillations are quickly damped, after which the damping force disappears, allowing the balance to be very sensitive.  Since eddy currents and magnetic damping occur only in conductors, recycling centers can use magnets to separate metals from other materials. Trash is dumped in batches down a ramp, beneath which lies a powerful magnet. Conductors in the trash are slowed by magnetic damping while nonmetals in the trash move on, separating from the metals. Other major applications of eddy currents are in metal detectors and braking systems in trains and roller coasters.  Portable metal detectors (Figure ) consist of a primary coil carrying an alternating current and a secondary coil in which a current is induced. An eddy current will be induced in a piece of metal close to the detector which will cause a change in the induced current within the secondary coil, leading to some sort of signal like a shrill noise. Braking using eddy currents is safer because factors such as rain do not affect the braking and the braking is smoother. However, eddy currents cannot bring the motion to a complete stop, since the force produced decreases with speed.  Induction cooktops have electromagnets under their surface. The magnetic field is varied rapidly producing eddy currents in the base of the pot, causing the pot and its contents to increase in temperature. Induction cooktops have high efficiencies and good response times but the base of the pot needs to be ferromagnetic, iron or steel for induction to work. Electric Generators Electric generators induce an emf by rotating a coil in a magnetic field. A generator with a single rectangular coil rotated at constant angular velocity in a uniform magnetic field produces an emf that varies sinusoidally in time. Note the generator is similar to a motor, except the shaft is rotated to produce a current rather than the other way around.  Charges in the wires of the loop experience the magnetic force, because they are moving in a magnetic field. Charges in the vertical wires experience forces parallel to the wire, causing currents. But those in the top and bottom segments feel a force perpendicular to the wire, which does not cause a current. This is just because the force applied there would be perpendicular to the charges. therefore no work is done on the charges so they dont move and make a current Thus, 𝑒𝑚𝑓 = 𝑁𝐴𝐵 𝜔 𝑠𝑖𝑛𝜔𝑡 is the emf induced in a generator coil of turns and area rotating at a constant angular velocity in a uniform magnetic field This can also be expressed as 𝑒𝑚𝑓 = 𝑒𝑚𝑓𝑜 𝑠𝑖𝑛𝜔𝑡 Where, 𝑒𝑚𝑓𝑜 = 𝑁𝐴𝐵 𝜔 ,is the maximum peak emf. The greater the number of coils, the larger their area, and the stronger the field, the greater the output voltage. It is interesting that the faster the generator is spun (greater ), the greater the emf. 3. A 60Hz AC generator rotates in 0.25T magnetic field. The generator consist of circular coil of radius 10cm with 100 loops. A) What is the angular velocity B) Calculate the maximum peak induced emf. Angular velocity = 2 x pi x hz emf = NAB x angular velocity Angular velocity = 377 rad/s emf = (100)(0.0314) (0.25) ( 377) emf = 296.1 V  All this is is when you have a generator or motor that has a flow of current do to a magnetic field, the current produced will oppose the magnetic field. Back Emf The motors and generators are very similar. Generators convert mechanical energy into electrical energy, whereas motors convert electrical energy into mechanical energy. Furthermore, motors and generators have the same construction. When the coil of a motor is turned, magnetic flux changes, and an emf is induced. The motor thus acts as a generator whenever its coil rotates. This will happen whether the shaft is turned by an external input, like a belt drive, or by the action of the motor itself.  That is, when a motor is doing work and its shaft is turning, an emf is generated. Lenz’s law tells us the emf opposes any change, so that the input emf that powers the motor will be opposed by the motor’s self-generated emf, called the back emf of the motor.  Back emf is the generator output of a motor, and so it is proportional to the motor’s angular velocity. It is zero when the motor is first turned on, meaning that the coil receives the full driving voltage and the motor draws maximum current when it is on but not turning. As the motor turns faster and faster, the back emf grows, always opposing the driving emf, and reduces the voltage across the coil and the amount of current it draws. When a vacuum cleaner, refrigerator, or washing machine is first turned on, lights in the same circuit dim briefly due to the IR drop produced in feeder lines by the large current drawn by the motor. If the motor runs at too low a speed, the larger current can overheat it perhaps even burning it out. If there is no mechanical load on the motor, it will increase its angular velocity until the back emf is nearly equal to the driving emf. Transformers Transformers do what their name implies—they transform voltages from one value to another. For example, many cell phones, laptops, video games, and power tools and small appliances have a transformer built into their plug-in unit that changes 120 V or 240 V AC into whatever voltage the device uses.  Transformers are also used at several points in the power distribution systems, such as illustrated in Figure. Power is sent long distances at high voltages, because less current is required for a given amount of power, and this means less line loss, as was discussed previously. But high voltages pose greater hazards, so that transformers are employed to produce lower voltage at the user’s location.  The type of transformer considered is based on Faraday’s law of induction as shown in figure. The two coils are called the primary and secondary coils. In normal use, the input voltage is placed on the primary, and the secondary produces the transformed output voltage. Not only does the iron core trap the magnetic field created by the primary coil, its magnetization increases the field strength. Since the input voltage is AC, a time-varying magnetic flux is sent to the secondary, inducing its AC output voltage.  The output voltage Vs depends almost entirely on the input voltage Vp and the ratio of the number of loops in the primary and secondary coils. Faraday’s law of induction for the secondary coil gives its induced output voltage Vs to be ΔΦ 𝑉𝑆 = −𝑁𝑠 Δ𝑡 ΔΦ where 𝑁𝑠 is the number of loops in the secondary coil and is the rate Δ𝑡 of change of magnetic flux. The input primary voltage Vp is also related to changing flux by, ΔΦ 𝑉𝑃 = −𝑁𝑃 Δ𝑡  Assuming negligible coil resistance, Kirchhoff’s loop rule tells us that the induced emf exactly equals the input voltage. Taking the ratio of these last two equations yields a useful relationship: 𝑉𝑠 𝑁𝑆 = 𝑉𝑃 𝑁𝑃 This is known as the transformer equation, and it simply states that the ratio of the secondary to primary voltages in a transformer equals the ratio of the number of loops in their coils. The output voltage of a transformer can be less than, greater than, or equal to the input voltage, depending on the ratio of the number of loops in their coils.  A step-up transformer is one that increases voltage, whereas a step- down transformer decreases voltage. Assuming, as we have, that resistance is negligible, the electrical power output of a transformer equals its input. This is nearly true in practice—transformer efficiency often exceeds 99%. Equating the power input and output, 𝑃𝑃 = 𝐼𝑃 𝑉𝑃 = 𝐼𝑆 𝑉𝑆 = 𝑃s Rearranging terms gives, 𝑉𝑆 𝐼𝑃 = 𝑉𝑃 𝐼𝑆  𝑉𝑠 𝑁𝑆 Combining with = gives, 𝑉𝑃 𝑁𝑃 Ip/Is = Np/Ns 𝐼𝑆 𝑁𝑃 = 𝐼𝑃 𝑁𝑆 is the relationship between the output and input currents of a transformer. So if voltage increases, current decreases. Conversely, if voltage decreases, current increases. 4. A transformer has 50 primary turns and 400 secondary turns. The input voltage is 12V and input current is 24A. a) what is the voltage and current at secondary coil? b) How much power is consumed by primary coil. Vs/Vp = Ns/Np P = IV P = 24 x 96 Vs/12 = 400/50 P =2304 W vs = (400/50) x 12 vs = 96 V 5. A 200W ideal transformer has primary voltage of 40V and secondary current of 20A. A) calculate the input current and output voltage. B) Is this step-up or step-down transformer? C) If there are 80 turns in primary coil, How many turns are there in secondary coil? P = IV Vs/Vp = Ip/Is Vs/Vp = Ns/ Np 20/40 = Ns / 80 I = P/V Vs/40 = 5/20 Ns = 40 turns I = 200 / 40 Vs = (5/20) x 40 Vs = 20 V I=5 A This is a step down as it goes from 40 volts input to 20 volts output