Induced emf - Engineering Physics - Lecture Slides, Slides of Engineering Physics

Download Induced emf - Engineering Physics - Lecture Slides and more Slides Engineering Physics in PDF only on Docsity! Today’s agenda: Induced emf. You must understand how changing magnetic flux can induce an emf, and be able to determine the direction of the induced emf. Faraday’s Law. You must be able to use Faraday’s Law to calculate the emf induced in a circuit. Lenz’s Law. You must be able to use Lenz’s Law to determine the direction induced current, and therefore induced emf. Generators. You must understand how generators work, and use Faraday’s Law to calculate numerical values of parameters associated with generators. Back emf. You must be able to use Lenz’s law to explain back emf. docsity.com Induced emf and Faraday’s Law Magnetic Induction We have found that an electric current can give rise to a magnetic field… I wonder if a magnetic field can somehow give rise to an electric current… docsity.com  A changing current in a loop of wire In the this case, nothing observable (to your eye) is moving, although, of course microscopically, electrons are in motion. Induced emf is produced by a changing magnetic flux. changing I changing B induced I gives rise to a changing magnetic field (predicted by Ampere’s law) which can induce a current in another nearby loop of wire. docsity.com Today’s agenda: Induced emf. You must understand how changing magnetic flux can induce an emf, and be able to determine the direction of the induced emf. Faraday’s Law. You must be able to use Faraday’s Law to calculate the emf induced in a circuit. Lenz’s Law. You must be able to use Lenz’s Law to determine the direction induced current, and therefore induced emf. Generators. You must understand how generators work, and use Faraday’s Law to calculate numerical values of parameters associated with generators. Back emf. You must be able to use Lenz’s law to explain back emf. docsity.com We can quantify the induced emf described qualitatively in the last few slides by using magnetic flux. Experimentally, if the flux through N loops of wire changes by dB in a time dt, the induced emf is Bd = - N . dt ε Faraday’s law of induction is one of the fundamental laws of electricity and magnetism. I wonder why the – sign… Faraday’s Law of Magnetic Induction Your text, pages 997-998, shows how to determine the direction of the induced emf. Argh! Lenz’s Law, coming soon, is much easier.   B average = - N . t ε docsity.com Possible homework hint: if B varies but loop  B. B Bd B dA B(t) dA        Ways to induce an emf:  change B  change the area of the loop in the field Possible homework hint: for a circular loop, C=2R, so A=r2=(C/2)2=C2/4, so you can express d(BA)/dt in terms of dC/dt. docsity.com Possible Homework Hint. I The magnetic field is not uniform through the square loop, so you can’t use BA to calculate the flux. Take an infinitesimally thin strip. Then the flux is d = BdAstrip. Integrate from a to b to get the flux through the strip. a b docsity.com Ways to induce an emf (continued):  change the orientation of the loop in the field =90 =45 =0 docsity.com In which direction is the current induced in the coil for each situation shown? (counterclockwise) (no current) Practice with Lenz’s Law. docsity.com c Pulling the coil to the right out of a magnetic field that points out of the page (counterclockwise) & @ ® 2((e))o ® @ ® 4 (a) Shrinking a coil in a magnetic field pointing into the page (clockwise) docsity.com Rotating the coil about the vertical diameter by pulling the left side toward the reader and pushing the right side away from the reader in a magnetic field that points from right to left in the plane of the page. (counterclockwise) docsity.com Motional emf: an overview An emf is induced in a conductor moving in a magnetic field. Your text introduces four ways of producing motional emf.   B d = - dt side view B A  1. Flux change through a conducting loop produces an emf: rotating loop.    = NBA sin tε     NBA I= sin t R   P= INBA sin t start with this derive these docsity.com 2. Flux change through a conducting loop produces an emf:   B d = - dtv ℓ B                               x=vdt dA MF = I B = B vε ε B v I = = R R PP = F v =I Bv start with these derive these expanding loop. docsity.com 3. Conductor moving in a magnetic field experiences an emf:  F= q E+v B v ℓ B                               – + = E (Mr. Ed) start with these derive this ε= B v You could also solve this using Faraday’s Law by constructing a ―virtual‖ circuit using ―virtual‖ conductors. magnetic force on charged particles. docsity.com Generators and Motors: a basic introduction Take a loop of wire in a magnetic field and rotate it with an angular speed . S N side view B A     B =B A = BA cos Choose 0=0. Then    0= t = t .   B = BA cos t Bd = - dt ε Generators are an application of motional emf. docsity.com If there are N loops in the coil Bd = - N dt ε   d BA cos t = - N dt ε    = NBA sin tε side view B A  || is maximum when  = t = 90° or 270°; i.e., when B is zero. The rate at which the magnetic flux is changing is then maximum. On the other hand,  is zero when the magnetic flux is maximum. The NBA equation! docsity.com emf, current and power from a generator    = NBA sin tε     NBA I= = sin t R R ε   P= I = INBA sin tε None of these are on your starting equation sheet! docsity.com Recall that one of the ways to induce an emf is to change the area of the loop in the magnetic field. Let’s see how this works. v ℓ B                               vdt dA A U-shaped conductor and a moveable conducting rod are placed in a magnetic field, as shown. The rod moves to the right with a constant speed v for a time dt. The rod moves a distance v dt and the area of the loop inside the magnetic field increases by an amount dA = ℓ v dt . Another Kind of Generator: A Slidewire Generator x docsity.com Bd = - N dt ε  d BA = 1 dt ε B dA = dt ε dx = B dt ε = B v . ε B and v are vector magnitudes, so they are always +. Wire length is always +. You use Lenz’s law to get the direction of the current. v ℓ B                               vdt dA The loop is perpendicular to the magnetic field, so the magnetic flux through the loop is B = = BA. The emf induced in the conductor can be calculated using Faraday’s law: B dA x docsity.com The induced emf causes current to flow in the loop. v ℓ B                               vdt dA Magnetic flux inside the loop increases (more area). System ―wants‖ to make the flux stay the same, so the current gives rise to a field inside the loop into the plane of the paper (to counteract the ―extra‖ flux). Clockwise current! I Direction of current? x docsity.com You might find it useful to look at Dr. Waddill’s lecture on Faraday’s Law, from several semesters back. Click here to view the lecture. If the above link doesn’t work, try copying and pasting this into your browser address bar: http://campus.mst.edu/physics/courses/24/Handouts/Lec_18.ppt docsity.com Let’s look in detail at each of these four ways of using motion to produce an emf. Method 3… docsity.com Motional emf is the emf induced in a conductor moving in a magnetic field. Example 3 of motional emf: moving conductor in B field. v ℓ B                               If a conductor (purple bar) moves with speed v in a magnetic field, the electrons in the bar experience a force  MF = qv B= -ev B The force on the electrons is ―up,‖ so the ―top‖ end of the bar acquires a net – charge and the ―bottom‖ end of the bar acquires a net + charge. The charges in the bar are ―separated.‖ ―up‖ – + This is a simplified explanation but it gives you the right ―feel.‖ docsity.com Let’s look in detail at each of these four ways of using motion to produce an emf. Method 4… docsity.com Example 4 of motional emf: flux change through conducting loop. (Entire loop is moving.) I’ll include some numbers with this example. Remember, it’s the flux change that produces the emf. Flux has no direction associated with it. However, the presence of flux is due to the presence of a magnetic field, which does have a direction, and allows us to use Lenz’s law to determine the ―direction‖ of current and emf. docsity.com                                                                                                     B = 0.6 T 5 c m A square coil of side 5 cm contains 100 loops and is positioned perpendicular to a uniform 0.6 T magnetic field. It is quickly and uniformly pulled from the field (moving  to B) to a region where the field drops abruptly to zero. It takes 0.10 s to remove the coil, whose resistance is 100 . docsity.com The induced emf is Bd d(BA) dA = - N = - N = - N B dt dt dt ε                                           v dA  d xdA dx = = = v dt dt dt x x docsity.com            m = 100 0.6 T 0.05 m 0.5 s ε = 1.5 Vε ―uniformly‖ pulled = - N B vε   x 5 cm m v = = = 0.5 t 0.1 s s The induced current is I = = = 15 mA . R 100 Ω ε 1.5 V docsity.com Current flows ―only*‖ during the time flux changes. E = P t = I2R t = (1.5x10-2 A)2 (100 ) (0.1 s) = 2.25x10-3 J *Remember: if there were no resistance in the loop, the current would flow indefinitely. However, the resistance quickly halts the flow of current once the magnetic flux stops changing. The loop has to be ―pulled‖ out of the magnetic field, so there is a pulling force, which does work. The ―pulling‖ force is opposed by a magnetic force on the current flowing in the wire. If the loop is pulled ―uniformly‖ out of the magnetic field (no acceleration) the pulling and magnetic forces are equal in magnitude and opposite in direction. (c) How much energy is dissipated in the coil? (d) Discuss the forces involved in this example. docsity.com                                                                                                     No flux change. No emf. No current. (No work.) docsity.com Remember, a force is needed only when the coil is partly in the field region. (e) Calculate the force necessary to pull the coil from the field.                                                                                                     I docsity.com                                                                                                     magF = N IL B where L is a vector in the direction of I having a magnitude equal to the length of the wire inside the field region. I L1 L2 L3 F1 F2 F3 Sorry about the ―busy‖ slide! The forces should be shown acting at the centers of the coil sides in the field. There must be a pulling force to the right to overcome the net magnetic force to the left. Fpull L4=0 Multiply by N because there are N loops in the coil. docsity.com If you build a generator and it doesn’t seem to be working… Handy Hint: Debugging Your Homemade Generator …or if you want to test a wall socket to see if it is ―live…‖ …simply purchase a Vilcus Plug Dactyloadapter from ThinkGeek ( http://www.thinkgeek.com/stuff/41/lebedev.shtml ) and follow the instructions. European model shown. US model also available. docsity.com Today’s agenda: Induced emf. You must understand how changing magnetic flux can induce an emf, and be able to determine the direction of the induced emf. Faraday’s Law. You must be able to use Faraday’s Law to calculate the emf induced in a circuit. Lenz’s Law. You must be able to use Lenz’s Law to determine the direction induced current, and therefore induced emf. Generators. You must understand how generators work, and use Faraday’s Law to calculate numerical values of parameters associated with generators. Skip to back emf (slide 68). Please study the next 5 slides on your own! Back emf. You must be able to use Lenz’s law to explain back emf. docsity.com electric motors and web applets Generator: source of mechanical energy rotates a current loop in a magnetic field, and mechanical energy is converted into electrical energy. Electric motor: a generator ―in reverse.‖ Current in loop in magnetic field gives rise to torque on loop. Other useful animations here. A dc motor animation is here. Details about ac and dc motors at hyperphysics. True Fact you didn’t know: all electrical motors operate on smoke. Every motor has the correct amount of smoke sealed inside it at the factory. If this smoke ever gets out, the motor is no longer functional. I can even provide the source of this true information. http://www.xs4all.nl/~jcdverha/scijokes/2_16.html#subindex docsity.com One more thing… This wire… …connects to this ring… …so the current flows this way. Another way to generate electricity with hamsters: give them little magnetic collars, and run them through a maze of coiled wires. http://www.xs4all.nl/~jcdverha/scijokes/2_16.html#subindex docsity.com Later in the cycle, the current still flows clockwise in the loop… …but now this* wire… …connects to this ring… …so the current flows this way. Alternating current! ac! Without commutator—―dc.‖ *Same wire as before, in different position. docsity.com Back emf. You must be able to use Lenz’s law to explain back emf. docsity.com If your house lights dim when an appliance starts up, that’s because the appliance is drawing lots of current and not producing a counter emf. Motors have design speeds their engineers expect them to run at. If the motor runs at a lower speed, there is less-than- expected counter emf, and the motor can draw more-than- expected current. When the appliance reaches operating speed, the counter emf reduces the current flow and the lights ―undim.‖ If a motor is jammed or overloaded and slows or stops, it can draw enough current to melt the windings and burn out. Or even burn up. docsity.com Induced emf on an airplane wing. Two brief examples (for you to review outside of lecture): Blood flow measurement. Please study these examples on your own! docsity.com                                     v Example: An airplane travels 1000 km/h in a region where the earth’s field is 5x10-5 T and is vertical. What is the potential difference induced between the wing tips that are 70 m apart? docsity.com