Phys. 122: Thursday, 03 Dec. Lots of stuff returned: please pick up yours in front. Written HW 13: Due by 5:00 pm. I will post solutions to HW 13 outside my office after today. Mast. Phys.: Assign. 10 (the last one!) due Monday of finals week (Dec. 07). An extra credit assignment is also available. Exam 3: there were 2 perfect scores; congratulations! Final Exam: Tuesday at 1:30 pm, right here. You may bring your calculator and 4 formula sheets; one from each of tests 1-3 and one new one. Study guide, sample problems, and sample cheat sheet are all available.

Faraday's Law in one final form, which is valid for any STATIONARY loop in space: This says that whenever a magnetic field changes with time, electric fields are generated! The electric fields are there in space no matter what (whether a conductor is there to make a current flow, or not).

Mutual Induction: A change in current in one circuit generates an EMF in the other. For Self-Induction, the original circuit is the SAME as the induced-EMF circuit! The SI unit of induction is the Henry, abbreviated H. Inductors give inertia to currents in circuits. ↱ L (or M)

Clickers: Inductor EMFs are conventionally drawn with “battery terminal” signs which show the equivalent battery polarity of the EMF. What is the current below doing? a) It is steady (constant) but nonzero b) It must be zero c) It must be increasing d) It must be decreasing e) The diagram as shown cannot be correct.

Remember that batteries try to “pump” current from their (–) terminal toward their (+) terminal!

Clickers: using our “fluid” analogy, an inductor most closely resembles... a) A water wheel (as for a flour mill) b) A partially blocked pipe c) A leak out of the side of a pipe d) Two tanks of water, stacked e) A drain

Power (=energy/time being either STORED or RELEASED) in an inductor:

Energy storage in inductors can be accounted for as energy stored in their magnetic field! (This should remind you of capacitors, whose stored energy can be accounted in their electric fields.) As with the capacitor case, this magnetic field energy formula is ALWAYS TRUE. In particular, electromagnetic waves (ch. 34) have energy in both their electric and their magnetic fields.

Clickers: If we have a circuit with inductors (L) in series or parallel, how do we construct rules for the equivalent circuits? a) The rules are like those for capacitors b) The rules are like those for resistors c) The series rules are similar to resistors, and the parallel rules are similar to capacitors d) The parallel rules are similar to resistors, and the series rules are similar to capacitors e) Inductors cannot be put into series or parallel

Capacitor and Inductor together (section 33.9): produce oscillations in voltage and current!

One very useful application of an LC circuit:

When induction is present, we have to modify Kirchhoff's Loop Rule! Inductive E fields go “downhill in a circle”, unlike static fields (that come from charges), so things in parallel might not have the same EMF drop.

Clickers: Every 11 years, we have to worry about induction in circuits due to what? a) El Ni ñ o storms here on Earth b) Volcanic activity here on Earth which triggers cicad insects to multiply c) Motion of the inner moons of Jupiter d) Magnetic storms from the moon e) Magnetic storms from the Sun

Shortcut “right-hand rules” for Faraday and Ampre: R.H. thumb along changing B direction gives R.H. fingers curling OPPOSITE to induced E (Lenz' Law), in Faraday. R.H. thumb along changing E direction or current I direction gives R.H. fingers curling WITH induced B, in Ampre.

Electromagnetic “Plane Waves”: possible in theory due to Maxwell's fix of Ampere's law.

Different frequencies of EM radiation get different names...

Clickers: The sun gives off all frequencies of electromagnetic radiation (even though we only see visible frequencies with our eyes). Which frequencies are the sun's brightest? a) In the AM radio band b) In the X-ray region c) In the ultraviolet region d) Yellow light, in the visible region e) Gamma rays of very high energy

Some Wave Definitions: Period (T) is the time for one full cycle. Wavelength ( λ ) is the distance for one cycle. So, ω and k convert time and distance into angle in radians, which we can take “cos” of: Both the electric and magnetic fields wiggle like “y” above, for an electromagnetic wave. This last equation is the key to how light changes direction when travelling into different materials.

The flow of electromagnetic energy with time is described by the Poynting Vector S, which gives the power per area perpendicular to S (equal to the energy flowing per time per area). This definition holds for all electric and magnetic fields --- not just in waves, but also in circuits! Closely related is the Intensity I, defined as the time-averaged value of S.

Polarization of an electromagnetic wave is the direction of the electric field of the wave.

When polarized light goes through another polarizer at angle θ to the first direction, only cos ² θ of the original Poynting vector and intensity make it through (Malus' Law). Half of unpolarized light makes it through any polarizer (and becomes polarized in the process).

Results from Maxwell's equations: the plane waves only satisfy the equations if all of the following are true: S must point in direction of wave propagation. E and B must be perpendicular to one another, and each perpendicular to S. |E| = (c/n) |B|. Wave speed v wave = c/n. Note that any frequency and wavelength are possible (as long as their product is c/n).

Evaluations: please fill out CRN for YOUR recitation section: : (Tues. afternoon) : (Wed. 1 pm) : (Wed. 3:30 pm) Instructor: Arendt GOOD LUCK WITH FINALS!!