1. Today’s Concept: Faraday’s Law Lenz’s Law
Physics 2112 Unit 17
Today’s Concept:
Faraday’s Law
Lenz’s Law

2. Define Magnetic Flux, FB
The Plan
Define Magnetic Flux, FB
Introduce Faraday’s Law in terms of magnetic flux
Do some examples to show how Faraday’s Law explains motional emf results we had last time.

3. Similar to electric flux FE
Define FB
Magnetic Flux: A B
Similar to electric flux FE
Think of FB as the number of field lines passing through the surface

4. Example 17.1 (Magnetic Flux)B
5cm
A copper disk with radius 5cm is placed in a magnetic field of uniform strength 0.2T.
What is the magnetic flux through the disk?

5. Notice Units: = T * m2 = N / C /(m/sec) * m2 = (V/m)/(m/sec) * m2
= V*sec

6. The emf will make a current flow if it can (like a battery).
Faraday’s Law:
In Words:
When the flux FB through a loop changes, an emf is induced in the loop.
The emf will make a current flow if it can (like a battery). I
Magnetic fields alone don’t cause currents
Changing magnetic fields cause currents

7. Three ways to change flux
Faraday’s Law
Three ways to change flux
Change |A|
Change |B|
Change the angle between the two

8. Example 17.2 (Change |B|)
A 10cm X 20m loop is formed by a motionless conducting bar (green) rests on two frictionless wires connected by a resistor R = 50W.
The entire apparatus is placed in a magnetic field that varies from 0 to 1.2 T in 30 seconds.
x x x x x x x x
B varies
What is the current through the resistor?

9. Example 17.3 (Change Area)
A 10cm conducting bar (green) rests on two frictionless wires connected by a resistor R = 50W. The entire apparatus is placed in a uniform magnetic field of 0.5 T pointing into the screen.
x x x x x x x x
The bar is pulled to the right by a force, F, at a velocity of 8m/sec.
What is the current through the resistor?

10. 17.4 (Change the angle)
A 10cm X 20 cm loop is rotated at 10rev/sec in a magnetic field of 0.1T.
If the loop is connected to a R = 50W resistor, what is the current?

11. Lenz’s Law
In words:
Whenever the magnetic flux through a surface changes a current is formed which creates a magnetic field which opposes that change.

12. CheckPoint 1
Suppose a current flows in a horizontal conducting loop in such a way that the magnetic flux produced by this current points upward.
As viewed from above, in which direction is this current flowing?

13. CheckPoint 2
A magnet makes the vertical magnetic field shown by the red arrows. A horizontal conducting loop is entering the field as shown.
At the instant shown below left, what is the direction of the additional flux produced by the current induced in the loop?

14. CheckPoint 3
A magnet makes the vertical magnetic field shown by the red arrows. A horizontal conducting loop is entering the field as shown.
The upward flux through the loop as a function of time is shown by the blue trace. Which of the red traces below it best represents the current induced in the loop as a function of time as it passes over the magnet? (Positive means counter-clockwise as viewed from above):

15. Induced electric field is not conservative!
A point of confusion….
Faraday’s Law:
Note:
Induced electric field is not conservative! 

16. Example 17.5 (Bar on Ramp)
A square metal bar has a length of 1m and a mass 1.2kg and slides down between two legs of a conducting U shaped rail that is at an angle of 45o to the ground.
Side view
45o
Top view
The entire rails/rod system has a resistance of 2.5W and is contained in a vertical 0.7T magnetic field.
What is the maximum velocity of the rod?

17. Example 17.6 (solenoid)
A long solenoid has 220 turns/cm and carries a current I=1.5A. It’s diameter is 3.2cm. At the center, we place a closely packed coil, C, with 32 turns that is 2.1cm in diameter.
The current in the solenoid is reduced to zero in 25ms.
What is the magnitude of the EMF induced in the coil while the current in the solenoid is changing?

18. Executive Summary: Faraday’s Law:
where
Executive Summary:
emf → current → field a) induced only when flux is changing
b) opposes the change

19. Remember?

20. A Change…..
Electricity and magnetism are now connected!