1. From last time… Faraday: Lenz: induced currents oppose change in flux
Tue. Nov. 4, 2008
Physics 208, Lecture 19

2. Faraday’s law EMF no longer zero around closed loop EMF around loop
Magnetic flux through surface bounded by path
Make comparison to battery. Show that this acts just like battery. Maybe use shaking flashlight to show that this works.
EMF no longer zero around closed loop
Tue. Nov. 4, 2008
Physics 208, Lecture 19

3. Lenz’s law Induced current produces a magnetic field. Lenz’s law
Interacts with bar magnet just as another bar magnet
Lenz’s law
Induced current generates a magnetic field that tries to cancel the change in the flux.
Here flux through loop due to bar magnet is increasing. Induced current produces flux to left.
Force on bar magnet is to left.
Do demo with magnet and copper plate. Copper plate in nitrogen.
Tue. Nov. 4, 2008
Physics 208, Lecture 19

4. Question
Which way is the magnet moving if it is inducing a current as shown?
A. Up
B. Down S N
Current creates flux up. This must be opposing increase in flux down. So magnet must be falling down N S
Tue. Nov. 4, 2008
Physics 208, Lecture 19

5. Question SN
As current is increasing in the solenoid, what direction will current be induced in ring?
A. Same as solenoid
B. Opposite of solenoid
C. No current
Tue. Nov. 4, 2008
Physics 208, Lecture 19

6. What is the direction of the force on the can?
Question
What is the direction of the current induced in the can?
Into page
Out of page CW
CCW
None of the above
Can
Coil I
Ican?
End view
What is the direction of the force on the can?
Tue. Nov. 4, 2008
Physics 208, Lecture 19

7. A copper guillotine blade falls toward a victim
A copper guillotine blade falls toward a victim. It enters field from strong magnets on way down. v
What is the direction of the current induced in the loop (blade) as it enters field? CW
CCW
Depends on field direction
What is the direction of the magnetic force on the blade?
After questions, do demo. Then ask how induced current and force depends on blade velocity. Then argue that blade reaches terminal velocity. Up
Down
Depends on field direction.
Tue. Nov. 4, 2008
Physics 208, Lecture 19

8. Eddy current braking Shinkansen Electro- magnets Steel Rail
ICE 3 near the Oberhaider Wald Tunnel on the Cologne-Frankfurt high-speed rail line
Shinkansen
Tue. Nov. 4, 2008
Physics 208, Lecture 19

9. Eddy current separation
side view
top view
Tue. Nov. 4, 2008
Physics 208, Lecture 19

10. Back to basics: solenoid flux
Uniform field inside
Change current -> change flux
N turns
Wire turns
Surface for flux
Tue. Nov. 4, 2008
Physics 208, Lecture 19

11. Magnetic flux in a solenoid
N=# of turns, =length of solenoid
Flux through one turn
=Flux through entire solenoid
inductance
Tue. Nov. 4, 2008
Physics 208, Lecture 19

12. Inductance: a general result
Flux = (Inductance) X (Current)
Change in Flux = (Inductance) X (Change in Current)
Faraday’s law:
Tue. Nov. 4, 2008
Physics 208, Lecture 19

13. Changing current in inductor
Ideal inductor:
Inductance, but zero resistance
Constant current:
Changing current:
Sign of across ideal inductor
Opposes change in current.
Inductor fights to keep a constant current
Tue. Nov. 4, 2008
Physics 208, Lecture 19

14. Energy stored in ideal inductor
Constant current (uniform charge motion)
No work required to move charge through inductor
Increasing current:
Work required to move charge across induced EMF
Total work
Energy stored in inductor
Tue. Nov. 4, 2008
Physics 208, Lecture 19

15. Magnetic energy density
Energy stored in inductor
Solenoid inductance
Energy stored in solenoid
Bsolenoid
Energy density
Tue. Nov. 4, 2008
Physics 208, Lecture 19

16. Question
A solenoid is stretched to twice its length while keeping the same current and same cross-sectional area. The stored energy
Increases
Decreases
Stays the same
B decreases by 2
Energy density decr by 4
Volume increases by 2
Tue. Nov. 4, 2008
Physics 208, Lecture 19