1. From last time… Magnetic flux dB dI
Magnetic field generated by current element: Biot-Savart dI dB r
Magnetic flux

2. Average = 64% B BC AB C A D Thur. Oct. 29, 2009
Physics 208, Lecture 17

3. Magnetic flux Magnetic flux is defined as
(Component of B  surface) x (Area element)
zero flux
Maximum flux
SI unit of magnetic flux is the Weber ( = 1 T-m2 )
Thur. Oct. 29, 2009
Physics 208, Lecture 17

4. Magnetic Flux
Magnetic flux  through a surface: (component of B-field  surface) X (surface area)
Proportional to # B- field lines penetrating surface
Thur. Oct. 29, 2009
Physics 208, Lecture 17

5. A magnetic flux analogy
Thur. Oct. 29, 2009
Physics 208, Lecture 17

6. Question
A ring of 1m cross-sectional area makes an angle of θ=60˚ with respect a 2T magnetic field.
The magnetic flux through the ring is
0.2 Weber
0.5 Weber
1.0 Weber
2.0 Weber
5.0 Weber
Uniform field gives
Thur. Oct. 29, 2009
Physics 208, Lecture 17

7. 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. 29, 2009
Physics 208, Lecture 17

8. 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. 29, 2009
Physics 208, Lecture 17

9. Nonuniform field from bar magnet
Moving the magnet changes flux through the ring.
Faraday effect predicts electric field in loop, which drives a current.
Thur. Oct. 29, 2009
Physics 208, Lecture 17

10. Question N
Which direction of motion does NOT induce a current in loop? W E
North
East
West
NorthEast S
Thur. Oct. 29, 2009
Physics 208, Lecture 17

11. 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. 29, 2009
Physics 208, Lecture 17

12. Electric potential difference
Work/charge to move charge against electric forces d b + a +
Example uniform electric field
Electric force on charge q
Work to move particle as shown
Electric potential difference
Thur. Oct. 29, 2009
Physics 208, Lecture 17

13. Electric fields from charges
Uniform E-field can arise from infinite charge sheet + +
These are called “Coulomb” electric fields
They are produced by charges
Thur. Oct. 29, 2009
Physics 208, Lecture 17

14. Question This electric field line could be generated by Point charge
Dipole charge
Plane of charge
Ring of charge
None of these
Thur. Oct. 29, 2009
Physics 208, Lecture 17

15. Making E-field by Faraday’s method
Thur. Oct. 29, 2009
Physics 208, Lecture 17

16. Different ways to make E-field
Coulomb electric field
Created by electric charges
Non-Coulomb electric field
Created by time-varying magnetic field
Thur. Oct. 29, 2009
Physics 208, Lecture 17

17. Question Faraday E-field Positive Negative Zero
You move a positive charge counterclockwise all the way around the circular path, returning to your starting point.
The work you have done is
Positive
Negative
Zero
Thur. Oct. 29, 2009
Physics 208, Lecture 17

18. EMF in a circuit, or along a path
Work done by E-field = So
is work per unit charge to
bring charge back to where it started.
Why didn’t we have something like this in electrostatics?
This is zero.
Thur. Oct. 29, 2009
Physics 208, Lecture 17

19. 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. 29, 2009
Physics 208, Lecture 17

20. 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. 29, 2009
Physics 208, Lecture 17

21. 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. 29, 2009
Physics 208, Lecture 17

22. 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. 29, 2009
Physics 208, Lecture 17

23. 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. 29, 2009
Physics 208, Lecture 17