Induction -->Inductors

1. Induction -->Inductors Back to Circuits for a bit …. Induction - Fall 2006

2. What the heck are we doing? • Today • 7:30 AM we had our problem review session • Continue on with Induction & Inductors • Watch those piling up WebAssigns! • Monday • More of the same, • Wednesday • EXAMINATION #3 • After Holiday • Complete the remaining six chapters in the syllabus. Induction - Fall 2006

3. The loop is pushed into a region where the magnetic field is into the page. The motion creates an induced current in the loop which in turn produces a magnetic field at A and B. • The field at A & B are the same. • The field at A is stronger than the one at B • The field at B is stronger than the one at A. • None of these. Induction - Fall 2006

4. Today we will consider a Coil Induction - Fall 2006

5. We will base our discussion on Faraday’s Law Lentz Induction - Fall 2006

6. Consider the following: • There are N turns in the solenoid. • There is a current flowing in the direction shown. • The power supply is set to 20 volts and the resistor is 10 ohms. • The coil wire has negligible resistance. Induction - Fall 2006

7. The steady state current (20 volts, 10 ohms) in the circuit is • 2 amperes • Less than 2 amperes • More than 2 amperes • Need more info. Induction - Fall 2006

8. A B The DIRECTION of the magnetic field in the coil is • From A to B • From B to A • Not enough information is given. Induction - Fall 2006

9. Back to the coil diagram … • Recall from the last discussion that the magnetic field in the coil is given by: • n = #turns per unit length • Coil is infinitely long • Sort of B Induction - Fall 2006

10. B Back to the coil diagram … • The Flux through a single turn of the coil is BA or m0niA. • Now, let’s increase the applied voltage linearly at a rate of DV/Dt. • The current will change at a rate DI/Dt. Induction - Fall 2006

11. B Back to the coil diagram … For the single coil (as Dt0) FARADAY Says: Induction - Fall 2006

12. B Looking into the coil from the end with the red arrow, the emf around the coil inducedcurrent will be • In a clockwise direction • In a counterclockwise direction Induction - Fall 2006

13. B So … the induced emf • Will create a current that will oppose the change in the current. • The induced emf will therefore oppose the applied voltage (also an emf) from the power supply. Induction - Fall 2006

14. So for the single coil Induction - Fall 2006

15. Definition of Inductance L UNIT of Inductance = 1 henry = 1 T- m2/A FB is the flux near the center of one of the coils making the inductor Induction - Fall 2006

16. An inductor in the form of a solenoid contains 420 turns, is 16.0 cm in length, and has a cross-sectional area of 3.00 cm2. What uniform rate of decrease of current through the inductor induces an emf of 175 μV? Induction - Fall 2006

17. Induction - Fall 2006

18. Look at the following circuit: • Switch is open • NO current flows in the circuit. • All is at peace! Let's close the switch.... Induction - Fall 2006

19. At the INSTANT that the switch is closed, the current through the resistor is: • Zero • E/R • Can’t tell Induction - Fall 2006

20. Three years after the switch is closed, the current through the resistor is: • E/R • Zero • Don’t care .. we will be out by then! Induction - Fall 2006

21. Graph? IR E/R Probably looks something Like this. time Induction - Fall 2006

22. Close the circuit… • After the circuit has been closed for a long time, the current settles down. • Since the current is constant, the flux through the coil is constant and there is no Emf. • Current is simply E/R (Ohm’s Law) Induction - Fall 2006

23. Close the circuit… • When switch is first closed, current begins to flow rapidly. • The flux through the inductor changes rapidly. • An emf is created in the coil that opposes the increase in current. • The net potential difference across the resistor is the battery emf opposed by the emf of the coil. Induction - Fall 2006

24. Looking at the math Induction - Fall 2006

25. Just as we did with the capacitor, we can solve this equation and we get: Induction - Fall 2006

26. The growth Induction - Fall 2006

27. Death of the current: Induction - Fall 2006

28. Graph Induction - Fall 2006

29. Consider the Solenoid Again… l n turns per unit length Induction - Fall 2006

30. Inductance & Geometry Depends only on geometry just like C and is independent of current. Induction - Fall 2006

31. Max Current Rate of increase = max emf VR=iR ~current Induction - Fall 2006

32. Solve the loop equation. Induction - Fall 2006

33. IMPORTANT QUESTION • Switch closes. • No emf • Current flows for a while • It flows through R • Energy is conserved (i2R) WHERE DOES THE ENERGY COME FROM?? Induction - Fall 2006

34. E=e0A/d +dq +q -q For an answerReturn to the Big C • We move a charge dq from the (-) plate to the (+) one. • The (-) plate becomes more (-) • The (+) plate becomes more (+). • dW=Fd=dq x E x d Induction - Fall 2006

35. The calc The energy is in the FIELD !!! Induction - Fall 2006

36. What about POWER?? power to circuit power dissipated by resistor Must be dWL/dt Induction - Fall 2006

37. So Energy stored in the Capacitor Induction - Fall 2006

38. WHERE is the energy?? l Induction - Fall 2006

39. Remember the Inductor?? ????????????? Induction - Fall 2006

40. So … Induction - Fall 2006

41. ENERGY IN THEFIELD TOO! Induction - Fall 2006

42. IMPORTANT CONCLUSION • A region of space that contains either a magnetic or an electric field contains electromagnetic energy. • The energy density of either is proportional to the square of the field strength. Induction - Fall 2006

43. END OF TOPIC Induction - Fall 2006