1. Chapter 20 Self-Inductance LR Circuits Motional EMF

5. V R + _ x x x 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 Law) will be I = V / R So, for some period of time, the current is changing from 0 to V / R. Changing Currents Changing Magnetic Fields

6. V R + _ x x x As a result of the changing current, the magnetic field that the current creates changes as well. That magnetic field passes through the plane of this circuit. There is a magnetic flux through the circuit.

7. The magnetic flux is changing as the current increases. An EMF is induced in the circuit as the current increases! And by Lenz’s Law, the induced EMF creates a current which opposes the changes in the magnetic flux. x x x V R + _

8. V R + _ Induced emf 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.

9. x x x V R + _ For the circuits we deal with in class, we generally ignore the self-inductance of the circuit itself. However, you might observe its effect on the circuits you construct in the laboratory. When you first put voltage across the circuit, the current should ramp up to its final value...

10. We will, however, pay attention to the self-inductance of a solenoid. When present as a circuit element, we call solenoids INDUCTORS. To power supply

11. What is an inductor (solenoid)? A bunch of current loops connected together! So a magnetic flux exists through the inductor. As 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.

12. Again, by Lenz’s Law, 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 l with N turns and a current I flowing through it?

13. What is the induced EMF through such a coil? Where L is the inductance and is defined to be

14. More generally, to define the inductance we can use AND TRUE ONLY FOR A SOLENOID!!!! That is, equate these two statements of the relationship of EMF to changing fluxes and changing currents.

15. General expression for self-inductance:

16. These are actual physics demonstrations taken from the closets of Chem/Phys and are meant for exhibition purposes, not for competition. NO WAGERING, PLEASE!

17. Induced current due to changing magnetic flux. LENZ’S LAW

18. Inductors set up a back-EMF in a circuit as the current in the circuit changes. The magnitude of that EMF is given by As 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.

19. Recall, 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

20. V R + _ L I t I = V /R I =0.632 V /R   = the time constant = L / R

21. We can use the loop rule and Ohm’s law to determine the voltage across the inductor. V = V L + V R Induced Back - EMF in the Inductor

23. x x x x x x L v What happens to the charges in this conducting bar as it moves with a constant velocity v through a uniform magnetic field? The positive charges within the conductor feel a magnetic force upwards. The negative charges feel a downwards force.

24. x x x x x x L v +++ --- F+F+ F-F- How long can charge be separated this way? Until the electrostatic force balances the magnetic force!

25. x x x x x x L v +++ --- F+F+ F-F- F E = F B F E = q E F B = q v B E = v B

26. x x x x x x L v What is the magnitude of the potential difference between the ends of the bar when the electrostatic and magnetic forces are in balance? |V| = E d = B L v