1. Physics 014
Induction

2. Faraday’s Law
Experiment #1

3. Faraday’s Law
Experiment #2

4. Faraday’s Law Current produced in loop is called the induced current
The work done per charge to produce the current is called the induced emf
The process of producing the current and emf is called induction

5. Faraday’s Law
An emf is induced in the loops when the number of magnetic field lines that pass through the loop is changing

6. Faraday’s Law
First, define the magnetic flux through a loop as

7. Faraday’s Law
The emf induced in a conducting loop is equal to the rate at which the magnetic flux through that loop changes with time.

8. Faraday’s Law
We may write Faraday’s law as

9. Faraday’s Law
For a coil of N turns

10. ???
The graph shows B(t) of a uniform magnetic field throughout a conducting loop with the direction perpendicular to the plane of the loop. Rank the regions of the graph according to the magnitude of the induced emf.

11. Faraday’s Law
Lenz’s law: An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current

12. Faraday’s Law
Field due to current opposes flux change

13. ???
For three situations in which identical circular conducting loops are in uniform magnetic fields that are increasing or decreasing in magnitude at identical rates. Rank the situations according to the magnitude of the induced current in the loops

14. Faraday’s Law

15. Faraday’s Law From the above reasoning we conclude that:
A changing magnetic field produces an electric field

16. Faraday’s Law
We may now rewrite Faraday’s law as,

17. ???
For the regions, a uniform magnetic field extends directly out of or into the page, with the direction indicated only for a. The field is increasing in magnitude the same in all regions (same areas too). Determine the direction of the field in all regions.

18. Inductors and Inductance
An inductor is typically a type of solenoid

19. Inductors and Inductance
For an inductor with N turns, a current i producing a flux ΦB The inductance is

20. Inductors and Inductance
The SI unit of inductance is the henry
1 henry = 1 H = 1 T m2/A

21. Inductors and Inductance
Applying Faraday’s law to an inductor:
An induced emf appears in any coil in which the current is changing

22. Inductors and Inductance
Combining the definition of inductance and Faraday’s law

23. Inductors and Inductance

24. Energy in a magnetic field
Just as a capacitor stored energy in an electric field, an inductor stores energy in a magnetic field

25. ???
For the induced emf in the coil, which describes the current through the coil: (a) constant and rightward, (b) constant and leftward, (c) increasing and rightward, (d) decreasing and rightward, (e) increasing and leftward, (f) decreasing and leftward ?

26. RL circuits
Let’s now examine RL circuits,

27. RL circuits
For the switch connected to a in the diagram we find (rise of current)
where

28. RL circuits
For the case when the b terminal is connected (decaying current)

29. ???
For the circuits with three identical batteries, inductors and resistors, rank the circuits according to the current through the battery (a) just after the switch is closed and (b) a long time later.