1. From last time… Faraday: Inductance: flux = (inductance) x (current)
Thur. Nov. 6, 2008
Physics 208, Lecture 20

2. Inductance: a general result
Flux = (Inductance) X (Current)
Change in Flux = (Inductance) X (Change in Current)
Faraday’s law:
Thur. Nov. 6, 2008
Physics 208, Lecture 20

3. Question
The current through a solenoid is doubled. The inductance of the solenoid
Doubles
Halves
Stays the same
Thur. Nov. 6, 2008
Physics 208, Lecture 20

4. Question
The potential at a is higher than at b. Which of the following could be true?
A) I is from a to b, steady
B) I is from a to b, increasing
C) I is from a to b, decreasing
D) I is from b to a, increasing
E) I is from b to a, decreasing
Thur. Nov. 6, 2008
Physics 208, Lecture 20

5. Inductor circuit Induced EMF extremely high
Breaks down air gap at switch
Air gap acts as resistor
Thur. Nov. 6, 2008
Physics 208, Lecture 20

6. Perfect inductors in circuits
Constant current flowing
All Voltage drops = 0 I I?
EMF needed to drive current thru resistor
-IR + VL = 0 + -
Thur. Nov. 6, 2008
Physics 208, Lecture 20

7. RL circuits - I? + Current decreases in time Time constant
Slow for large inductance
(inductor fights hard, tries to keep constant current)
Slow for small resistance
(no inductor EMF needed to drive current)
Time constant
Thur. Nov. 6, 2008
Physics 208, Lecture 20

8. RL circuits - I(t) + Time constant Thur. Nov. 6, 2008
Physics 208, Lecture 20

9. 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. Nov. 6, 2008
Physics 208, Lecture 20

10. EMF and E.ds in electrostatics
Remember, work done by E-field = so y
“EMF” A
Integral of E-field around closed loop is zero in electrostatics x
Thur. Nov. 6, 2008
Physics 208, Lecture 20

11. Not only charges produce E-field Not only currents produce B-field
Gauss’ law: charges create E-fields
Ampere’s law: currents create B-fields
Time-dependent fields
Not only charges produce E-field
a changing B-field also produces an E-field
Not only currents produce B-field
a changing E-field produces a B-field
Thur. Nov. 6, 2008
Physics 208, Lecture 20

12. James Clerk Maxwell
Electricity and magnetism were originally thought to be unrelated
in 1865, James Clerk Maxwell provided a mathematical theory that showed a close relationship between all electric and magnetic phenomena
Thur. Nov. 6, 2008
Physics 208, Lecture 20

13. Maxwell’s Starting Points
Electric field lines originate on positive charges and terminate on negative charges (E  1 / R2)
Gauss’s law for E
Magnetic field lines always form closed loops – they do not begin or end anywhere
Gauss’s law for B
Magnetic fields are generated by moving charges or currents
Ampère’s Law
A varying magnetic field induces an emf and hence an electric field
Faraday’s Law
Thur. Nov. 6, 2008
Physics 208, Lecture 20

14. Maxwell’s Predictions
Electric and Magnetic fields play symmetric roles in nature
light waves consist of fluctuating electric and magnetic fields
each varying field induces the other
In vacuum, EM waves travel at speed of light : 3x108 m/s
Thur. Nov. 6, 2008
Physics 208, Lecture 20

15. Electric/magnetic fields perpendicular to propagation direction
A Transverse wave.
Electric/magnetic fields perpendicular to propagation direction
Can travel in empty space
f = v/, v = c = 3 x 108 m/s (186,000 miles/second!)
Thur. Nov. 6, 2008
Physics 208, Lecture 20

16. Electromagnetic Waves
E and B fields are perpendicular
to each other
to propagation direction
E and B fields are ‘in phase’
Both reach their peak values simultaneously
Wave moves in space
Propagation direction is
Thur. Nov. 6, 2008
Physics 208, Lecture 20

17. Question:
At a particular instant, an EM wave has an E-field pointing in the y-direction and a B-field pointing in the x-direction. The propagation direction is z z y X
D. -z
E. -y
F. -x y x
Thur. Nov. 6, 2008
Physics 208, Lecture 20

18. The EM Spectrum Note the overlap between types of waves
Visible light is a small portion of the spectrum
Types are distinguished by frequency or wavelength
Thur. Nov. 6, 2008
Physics 208, Lecture 20

19. Sizes of EM waves Visible light 230 m 0.044 m 2.3 m 44m
typical wavelength of 500 nm = = 0.5 x 10-6 m = 0.5 microns (µm)
AM 1310, your badger radio network, has a vibration frequency of 1310 KHz = 1.31x106 Hz
What is its wavelength?
230 m
0.044 m
2.3 m
44m
Thur. Nov. 6, 2008
Physics 208, Lecture 20

20. Hertz’s Confirmation of Maxwell’s Predictions
Generates and detected electromagnetic waves
Showed they have same properties as light waves
Thur. Nov. 6, 2008
Physics 208, Lecture 20

21. Hertz Trans & reciever EM wave Receiver spark gap
Transmitter spark gap
EM wave
Magnified view of the spark gap and dipole transmitting ("feed") antenna at the focal point of the reflector. The high voltage spark jumped the gap between the spherical electrodes. The electrical impulse produced by the spark generated damped oscillations in the dipole antenna.
Magnified view of the spark gap and dipole receiving antenna at the focal point of a receiving reflector similar to the transmitting one. The width of the small spark gap on the right is controlled by the screw below it. The vertical dipole antenna at the left was about 40 centimeters long.
Thur. Nov. 6, 2008
Physics 208, Lecture 20

22. Transatlantic signals
Capacitor banks
Induction coils
Spark gap
Gulgielmo Marconi’s transatlantic transmitter
Thur. Nov. 6, 2008
Physics 208, Lecture 20

23. Transatlantic receiver
Left to right: Kemp, Marconi, and Paget pose in front of a kite that was used to keep aloft the receiving aerial wire used in the transatlantic radio experiment.
Thur. Nov. 6, 2008
Physics 208, Lecture 20

24. EM Waves from an Antenna
Two rods are connected to an ac source, charges oscillate between the rods (a)
As oscillations continue, the rods become less charged, the field near the charges decreases and the field produced at t = 0 moves away from the rod (b)
The charges and field reverse (c)
The oscillations continue (d)
Thur. Nov. 6, 2008
Physics 208, Lecture 20

25. Detecting EM waves FM antenna AM antenna
Oriented vertically for radio waves
Thur. Nov. 6, 2008
Physics 208, Lecture 20

26. EM Waves Question?
Which direction should I orient my loop antenna to receive a signal from the transmission tower?
A) B) C) + -
Thur. Nov. 6, 2008
Physics 208, Lecture 20