Physics 152. Lenz s Law Practice Inductors. Announcements. Friday, April 27, 2007

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1 ics Fri pr.7. nnouncements enzs aw Practice Inductors Friday, pril 7, 007 Help sessions W 9-10 pm in NSC 119 Masteringics Hwk #5 due Fri., May 4 Final Exam available Friday, May 4 from Mrs. Wellsand. Fri pr.7. nnouncements Fri pr.7. nnouncements vailable Friday, May 4 Due by our scheduled exam period Monday, May 14 (10:30 am - 1:30 pm) Hint: Be able to do the homework (graded ND recommended) and you ll do fine on the exam! You may bring one 8.5 X11 index card (handwritten on both sides), a pencil or pen, and a scientific calculator with you. I will put any constants and mathematical formulas that you might need on a single page attached to the back of the exam. Section 1: graphical problem Section : conceptual problem Sections 3-6: One problem on Ch 3 One problem on Ch 33 Two problems on material from Exams 1 and EQUIED Multiple Choice Section: 10 questions covering all the above material, 6 on previous material, 4 on Chapters 3-34 Worksheet Problem #1 In which direction will the current flow? x x v x x x x x x x x x x x Two ways to answer this question: 1) The right-hand rule for moving charges in a uniform magnetic field. ) enz s aw 1

2 In which direction will the current flow? x x v x x x x x I x x x x x In which direction will the current flow? x x v x x x x x I x x x x x 1) The right-hand rule for moving charges in a uniform magnetic field. v to the right. B into the board. Force on the positive charge carriers is up. So the current will go around counterclockwise. ) enz s aw s the bar moves to the right, the flux through the loop into the board is increasing. The current in the loop must create flux out of the board. So the current goes counterclockwise. Worksheet Problems #, #3, and #4 circular loop is oriented with its plane perpendicular to a uniform magnetic field with B = 1.5 T. t an instant when the radius of the loop = 1.0 cm and is increasing at a rate of 3.0 cm/s, what is the magnitude of the EMF induced in the loop? B m m 4. 5 m m Worksheet Problem #5 What happens when the switch is first closed? What happens when the switch is first closed? Initially, there is no current in the circuit. We know the final current in this circuit (from Ohm s aw) will be I = / So, for some period of time, the current is changing from 0 to /. s a result of the changing current, the magnetic field that the current creates changes too. That magnetic field passes through the plane of this circuit. There is therefore a changing magnetic flux through the circuit.

3 What happens when the switch is first closed? The magnetic flux is changing as the current increases. n EMF is induced in the circuit! By enz s aw, the induced EMF results in a current that opposes the changes in magnetic flux. The very fact that the circuit is a closed loop made of conducting material has resulted in an induced EMF in the circuit which opposes the current! Of course, once the current attains its final value, the induced EMF = 0 because the magnetic field is no longer changing. Unless otherwise stated, we generally ignore the self-inductance of the circuit itself. However, you might observe its effect on the circuits you construct in the laboratory. We will pay attention to the self-inductance of a solenoid, which as a circuit element is called an INDUCTO When you put a potential difference across the circuit, the current should ramp up to its final value... To power supply To power supply What is an inductor (solenoid)? bunch of current loops connected together! So a magnetic flux exists through the inductor. s was the case with the electrical circuit of the last example, an induced EMF will be generated across the inductor when the current through the inductor changes. gain, by enz s aw, the induced EMF will generate a current to oppose the changing magnetic flux through the inductor. What is the magnetic flux through an inductor of length with N turns and a current I flowing through it? = N B N = Nμ 0 I = μ N 0 I 3

4 What is the induced EMF through such a coil? N = μ 0 TUE ONY FO SOENOID!!!! = d = di = μ 0 N di where is the inductance and is defined to be N = μ 0 We can derive another definition by combining = N d ND = di That is, equate these two statements of the relationship of EMF to changing fluxes and changing currents. = N I [] = Nm [] = [N] [] [I] [] = Tm = = Js C = s = H General expression for self-inductance Wb = turns N m m HENY Two solenoids have the same crosssectional area. Solenoid B, however, is twice as long and has twice the number of turns as Solenoid. The ratio of the self-inductance of Solenoid B to that of Solenoid is 1. 1 / 4. 1 / 3. 1 / 1 4. / / 1 Worksheet Problem #6 Inductors set up a back-emf in a circuit as the current in the circuit changes. The magnitude of that EMF is given by = di s a circuit element, therefore, inductors affect the rate at which the current in a circuit changes. In some respects, their effect on a circuit is analogous to the role of a capacitor. ecall, capacitors are circuit elements which store energy in an electric field between a positively charged plate and a negatively charged plate. Inductors store energy in a magnetic field. The amount of energy stored in the magnetic field of an inductor is given by U = 1 I 4

5 How do we go about deriving this? The power consumed by a circuit element is given by Plugging in the voltage across an inductor Power is energy per time, so we have P = I du P = I di = I di How do we go about deriving this? du Now, integrating both sides du = I di U = I di = 1 I et s set up Kirchhoff s loop equation: di I = 0 It = 0 This differential equation has a known solution given by e t /( / () ( ) = 1 ) I I=/ I=0.63/ = the time constant = / t Imax = / It () I ( e t / = 1 ) max We can use the loop rule and Ohm s law to determine the potential difference across the inductor: = (t) = I = I max (1 e t / ) = (1 et / ) t / () t = ( e 1 ) t () t = ( 1 e ) = e / t/ Induced Back - EMF in the Inductor 5

6 Worksheet Problem #7 In the circuit below, = 7.00 H, = 9.00, and = 10. What is the self-induced emf in the inductor 0.00 s after the switch is closed? Worksheet Problem #8 S 1 S If we now open switch S 1 and simultaneously close switch S, we once again have a changing current in our circuit, inducing an EMF across our inductor. This time, the loop rule says: = 0 di I = 0 with It I e t () = solution max /( / ) I I=/ I=0.8/ S 1 S If we allowed our previous circuit to reach its stable state t Imax = / It = I e t () max / = the time constant = / S 1 S Worksheet Problem #9 Using Ohm s aw and the loop rule we know = I = 0 = = e t / 6