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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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