Lecture 13.1 :! Electromagnetic Induction Continued Lecture Outline:! Faraday s Law! Induced Fields! Applications! Textbook Reading:! Ch. 33.5-33.7 April 7, 2015 1
Announcements! Homework #10 due on Tuesday, April 14, at 9am.! Finish reading Ch. 33 this week.! Questions? Concerns? Want to work on some practice problems? Come see me during office hours today from 3-5pm, or make arrangements for another day/time.! Final MidTerm (#3) of the semester is on Thursday, April 16, and will cover Ch. 32 and 33. Don t delay your studying! 2
Last Lectures... Faraday observed that a changing magnetic field creates an induced current. 3
Last Lectures... There is an induced emf (a.k.a. motional emf)in the moving conductor, with magnitude vlb. 4
Last Lecture... It is once again useful to introduce the idea of the flux of field (magnetic) passing through a current loop. For a uniform magnetic field m = A B Units of magnetic flux:! 1 weber = 1 Wb = 1 Tm 2 5
Last Lecture 6
Clicker Question #1 The bar magnet is pushed toward the center of a wire loop. Which is true? A. There is a clockwise induced current in the loop.! B. There is a counterclockwise induced current in the loop.! C. There is no induced current in the loop. 1. Upward flux from magnet is increasing. 2. To oppose the increase, the field of the induced current points down. 3. From the right-hand rule, a downward field needs a cw current. 7
Clicker Question #2 The current in the straight wire is decreasing. Which is true? A. There is a clockwise induced current in the loop.! B. There is a counterclockwise induced current in the loop.! C. There is no induced current in the loop. 1. The flux from wire s field is into the screen and decreasing. 2. To oppose the decrease, the field of the induced current must point into the screen. 3. From the right-hand rule, an inward field needs a cw current. 8
Faraday s Law Lenz s law lets us determine which direction an induced current will flow. We still don t know how to quantify the magnitude of the induced emf. We ve observed that the magnitude of the emf depends on a few things: strength of magnets; rate of change of magnetic field; area of currentcarrying loop. 9
Faraday s Law All induced currents are associated with a changing magnetic flux. Two ways flux can change:! 1.Geometry: Loop can expand, contract, or rotate.! 2.Magnetic field can change. m = A B E = d m dt = B da dt + A db dt 10
Faraday s Law: Demos Demos:! 1.) Rolling ball down a conductor.! 2.) Osheroff Magnet! 3.) Damped pendulum. 11
Faraday s Law Magnetic Braking used to sort metals out of recyclable truck. https:// www.youtube.com/ watch?v=ek6nphc4jd8 12
Applications Generators, such as those in hydroelectric dams, use induction to generate power (AC power). Changing flux through one loop of N-loop generator coil. m = A B = AB cos = AB cos t E coil = N d m dt = ABN d dt (cos t) = ABNsin t 13
Faraday s Law: Example Problem Two 20-turn coils are tightly wrapped around the same 2.0 cm diameter cylinder with 1.0mm diameter wire. The current through coil 1 is shown in the graph. Determine the current in coil 2 at t= 0.05s, and t=0.25s. Assume that a positive current is into the page at the top of the loop. 14
Applications Transformers allow voltages to be stepped-up or stepped-down. V 2 = N 2 N 1 V 1 15
Applications Another method of generating power Motion of magnet on a spring, surrounded by a coil, leads to induced current that charges a battery. 16
Induced Fields Magnetic forces alone cannot explain the current induced in a stationary loop by a changing magnetic field! We ve seen that induced emf develops since charge carriers in moving conductor are subject to a magnetic force (qv x B) If the conductor is not moving, but is in a changing magnetic field, how does the emf develop? 17
Induced Fields We know from Lenz s law that a conducting loop in a changing magnetic field will develop an induced current to counteract the changing flux. There must be an E-field present to create this current in the loop. In this changing magnetic field, the E-field is present whether or not the loop is there! 18
Induced Fields In other words,! there are two ways to create an electric field: Coulomb electric field is created by charges. non-coulomb electric field is created by changing magnetic field. 19
Clicker Question #3 The magnetic field is decreasing. Which is the induced electric field? The field is the same direction as induced current would flow if there were a loop in the field. E. There s no induced field in this case. 20
Reminders! Read all of Ch. 33! Homework #10 due on Tuesday, April 8.! Please take advantage of office hours, TAs, clinic etc 21