1. The story so far… dI dB r
Magnetic field generated by current element: Biot-Savart I
Ampere’s law
closed path
surface bounded by path

2. Exam 2 results Ave=70 Grade boundaries: A: 83 AB: 76 B: 67 BC: 57
Thur. Oct. 30, 2008
Physics 208, Lecture 18

3. Magnetic field from a current loop
One loop: field still loops around the wire.
Many loops: same effect
This is just like the elementary magnetic particle (dipole) we discussed earlier.
Thur. Oct. 30, 2008
Physics 208, Lecture 18

4. Building a solenoid
Thur. Oct. 30, 2008
Physics 208, Lecture 18

5. Ampere’s law for the solenoid
Thur. Oct. 30, 2008
Physics 208, Lecture 18

6. Ampere’s law Sum up component of B around path
Equals current through surface.
Component of B along path I
closed path
Ampere’s law
surface bounded by path
Thur. Oct. 30, 2008
Physics 208, Lecture 18

7. Gauss’ law in electrostatics
Electric flux through surface  charge enclosed
What about magnetic flux?
Thur. Oct. 30, 2008
Physics 208, Lecture 18

8. Magnetic flux Magnetic flux is defined exactly as electric flux
(Component of B  surface) x (Area element)
zero flux
Maximum flux
SI unit of magnetic flux is the Weber ( = 1 T-m2 )
Thur. Oct. 30, 2008
Physics 208, Lecture 18

9. Magnetic flux What is that magnetic flux through this surface?
Positive
Negative
Zero
Thur. Oct. 30, 2008
Physics 208, Lecture 18

10. Gauss’ law in magnetostatics
Net magnetic flux through any closed surface is always zero:
Compare to Gauss’ law for electric field
No magnetic ‘charge’, so right-hand side=0 for mag.
Basic magnetic element is the dipole
Thur. Oct. 30, 2008
Physics 208, Lecture 18

11. Time-dependent fields
Up to this point, have discussed only magnetic and electric fields constant in time.
E-fields arise from charges
B-fields arise from moving charges (currents)
Faraday’s discovery
Demonstrate by moving magnetic around in air, pointing to where electric fields were created. How did Faraday measure these electric fields?
Another source of electric field
Time-varying magnetic field creates electric field
Thur. Oct. 30, 2008
Physics 208, Lecture 18

12. Measuring the induced field
A changing magnetic flux produces an EMF around the closed path.
How to measure this?
Use a real loop of wire for the closed path.
The EMF corresponds to a current flow:
Thur. Oct. 30, 2008
Physics 208, Lecture 18

13. Current but no battery? Electric currents require a battery (EMF)
Faraday: Time-varying magnetic field creates EMF
Faraday’s law:
EMF around loop = - rate of change of mag. flux
Thur. Oct. 30, 2008
Physics 208, Lecture 18

14. 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
Thur. Oct. 30, 2008
Physics 208, Lecture 18

15. Quick quiz
Which of these conducting loops will have currents flowing in them? A. B.
Constant I
I(t) increases D. C.
Constant v
Constant v
Talk about magnetic fields generated by the induced currents, and what sense magnet that produces.
Constant I
Constant I
Thur. Oct. 30, 2008
Physics 208, Lecture 18

16. Faraday’s law Faraday’s law Biot-Savart law Result
Time-varying B-field creates E-field
Conductor: E-field creates electric current
Biot-Savart law
Electric current creates magnetic field
Result
Another magnetic field created
Thur. Oct. 30, 2008
Physics 208, Lecture 18

17. Thur. Oct. 30, 2008
Physics 208, Lecture 18

18. 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.
Thur. Oct. 30, 2008
Physics 208, Lecture 18

19. Demonstration: Faraday & Lenz

20. Quick quiz
What direction force do I feel due to Lenz’ law when I push the magnet down? Up
Down
Left
Right
Strong magnet
Copper
Thur. Oct. 30, 2008
Physics 208, Lecture 18

21. Quick Quiz
A conducting rectangular loop moves with constant velocity v in the +x direction through a region of constant magnetic field B in the -z direction as shown.
What is the direction of the induced loop current?
CCW CW
No induced current y x
Thur. Oct. 30, 2008
Physics 208, Lecture 18

22. Quick Quiz CCW CW No induced current
Conducting rectangular loop moves with constant velocity v in the -y direction away from a wire with a constant current I as shown. What is the direction of the induced loop current?
CCW CW
No induced current I v
B-field from wire into page at loop Loop moves to region of smaller B, so flux decreases Induced loop current opposes this change, so must create a field in same direction as field from wire -> CW current.
Thur. Oct. 30, 2008
Physics 208, Lecture 18

23. AC Generators N turns of same area rotating in a uniform B
The AC generator consists of
a loop of wire rotated by some
external means in a magnetic field
N turns of same area rotating in a uniform B
FB = BA cos q = BA cos wt
emf
max=NAB
In USA & Canada:
f=/(2)=60 Hz
In Europe f=50 Hz
Thur. Oct. 30, 2008
Physics 208, Lecture 18