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Lenz’s Lab Dr. Lenz strikes again. We looked at induced currents We indirectly covered Lenz’s Law Today we will explore induction further and learn about a new circuit element. Friday we will have a quiz. (Remember my threat … it might happen! Or not.) We looked at currents and magnetic fields induced by changing magnetic fields. We defined magnetic flux. We can now state Lenz’s Law in the following way: ◦ If you try to change the magnetic FLUX through a closed surface, the induced current will be in such a direction as to OPPOSE the change that you are trying to make! ◦ Or – “The toast will always fall buttered side down!” You said that there is a conducting loop. You said that there is therefore a current induced around the loop if the flux through the loop changes. But the beginning and end point of the loop are the same so how can there be a voltage difference around the loop? Or a current??? ‘tis a puzzlement! Induction 5/23/2017 4 Induction 5/23/2017 5 DID I LIE?? Induction 5/23/2017 6 Electric fields that are created by static charges must start on a (+) charge and end on a (–) charge as I said previously. Electric Fields created by changing magnetic fields can actually be shaped in loops. Induction 5/23/2017 7 Because you said that an emf is a voltage so if I put a voltmeter from one point on the loop around to the same point, I will get ZERO volts, won’t I? How can there be a current?? Induction 5/23/2017 8 Induction 5/23/2017 9 Is the WORK that an external agent has to do to move a unit charge from one point to another. But we also have (neglecting the sign): V Es s Induction 5/23/2017 10 emf Es E s x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x emf 2RE zero E Conductor Induction 5/23/2017 11 x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x E A B C The emf Zero Can’t tell A Conductor Induction 5/23/2017 12 emf MINUS???? Through the loop t Michael Faraday (1791-1867) Induction 5/23/2017 13 A: The way that you don’t want it to point! (Lenz’s Law). Lenz’s Law Explains the (-) sign! Induction 5/23/2017 14 In this case, 2 coils, each have the SAME emf so we add.. Ohm’s Law still works, so emf N t emf i Rcoil Induction 5/23/2017 15 Induction 5/23/2017 17 Induction 5/23/2017 18 Induction 5/23/2017 19 N B L i If the FLUX changes a bit during a short time t, then the current will change by a small amount i. Li N B Faraday says this is the emf! B i N L t t This is actually a calculus equation Induction 5/23/2017 20 i E= emf L t There should be a (-) sign but we use Lenz’s Law instead! The UNIT of “Inductance – L” of a coil is the henry. SYMBOL: Induction 5/23/2017 21 Induction 5/23/2017 22 Switch is open .. no current flows for obvious reasons. Switch closed for a long time: ◦ Steady current, voltage across the inductor is zero. All voltage (E) is across the resistor. ◦ i=E/R Induction 5/23/2017 23 When the switch opens, current change is high and back emf from L is maximu i E/R t As the current increases, more voltage is across R, the rate of change of I decrea and as the current increases, it increases more slowly. Induction 5/23/2017 24 When L=0, the current rises very rapidly (almost instantly) As L increases, it takes longer for the current to get to its maximum. Induction 5/23/2017 25 i emf iR L 0 i Solution E i (1 e ( R / L ) t ) R E i (1 e t / ) R L (time constant) R Induction 5/23/2017 26 1 1 0.63 e } 63% of maximum e= 2.71828… Induction 5/23/2017 27 Magnetic field begins to collapse, sending its energy into driving the current. The energy is dissipated in the resistor. i begins at maximum (E/R) and decays. Induction 5/23/2017 28 E t / i (e ) R Induction 5/23/2017 29