11We say that "concert A" corresponds to a frequency of 440 Hz.Does that mean that a flute playing concert A is emitting lowfrequency (440 Hz) electromagnetic radiation which we "hear"?A: Yes, sound is an electromagnetic wave.B: No, sound is not an electromagnetic wave.2CAPA #14 FridayReading: 34.8There is a new (and final!) online participation available._________________________Last: Maxwell's equationsToday: More of Maxwell and EM radiationNext: More on light and EM radiation3 ! v E " dv l Loop#= $ddtv B " dv A surface##And thus Faraday’s Law can be written as:Faraday's Law:! "= #d$magdt24CT 33.14A long solenoid (radius R) contains a uniform B field thatincreases steadily, B(t) = c t.Consider the dashed “Amperian loop”.What is around the loop? (going CCW)A: zeroB: 2πrEC: 2πRED: π r^2 EE: π R^2 E! E • dL"RrB5CT 33.14bWhat is through the the dashed curve?RrB! B •dA""A: zeroB: 2πrBC: 2πRBD: π r^2 BE: π R^2 B6CT 33.14cA: E=constant B: E ~ 1/rC: E ~ r D: E~ r^2E: OtherRrBLet’s put this together. Recall B = ct.Faraday saysRecall the left side is 2πrERecallSo… how does E depend on r?! E •dl = "d#dt= "ddt$B •dA$$! B •dA ="r##2B37Maxwell realized that Ampere’s Law must be incompletebecause he discovered a situation where it gave the wronganswer! ! v B " dv l #=µ0ithroughAmpere’s Law8Current iCurrent i+++++-----1. As the currents are flowing, one has Magnetic Fieldsaround the wires.2. Charge is also building up on the plates, creating anincreasing Electric Field between them.B BE9Current iCurrent i+++++-----B=?Clicker QuestionConsider the Biot-Savart Law for Magnetic Fields.Is there a Magnetic Field at the point labeled between the plates?A)Yes, there is a B-FieldB)No, there is zero B-field410CT 32.10iB=? ! dv B =µ0i4"dv L #ˆ r r2dLr+++++-----11Current iCurrent i+++++-----B=?Clicker QuestionNow consider an Amperian Loop as drawn. According toAmpere’s Law is there a Magnetic Field at the point labeledbetween the plates?A)Yes, there is a B-FieldB)No, there is zero B-fieldSomething must be wrong withAmpere’s Law! ! v B " dv l #=µ0ithrough12The changing Electric Field inside the capacitor must act likea current enclosed for Ampere’s Law.!"+=#dtdildBEenc 000$µµvvWhere !"=# AdEEvvdtdE!0"and is often called the “displacement current.”Thus, a changing Electric Field creates a Magnetic Field !513Current iCurrent i+++++-----B BE14These four equationsare called Maxwell’sequations.These are the axiomsof electromagnetism.They are one of themajor triumphs ofmodern science! ! r E • dv A ""= Qenclosed/#0r B • dv A ""= 0r E • dr l = $d%Bdt"r B • dr l =µ0ithrough+µ0#0d%Edt"15Oliver HeavisideMany times you will see the equations in a vector calculus form.616A shaking charge creates an electromagnetic wave. (Phet sim)Wave = self propagating disturbance2/1122700)/1085.8/104(1 vspeed!!!"""== mFAN#$µ! speed v = 3 "108m / s=c, Speed of Light !17Traveling wavex(position)λf λ = cλ /T = c18Visible Light: λ= 400 nm (violet) 700 nm (red)Example:λ = 500 nm (yellow)f = c/λ = 3x108/550x10-9 = 5x1014 Hz719Television transmissions are in the“radio” range.λ = 1-5 metersf =c/λ ~ 108 Hz = 100 MHzOn Television, different channels havedifferent frequencies and thus differentwavelengths. When you set thechannel knob, you amplify just thatfrequency range.20A radio wave of wavelength 2 meters passes by a person witha radio receiver. The person “watches” the electric andmagnetic fields go up and down as the wave travels past.After 1 second, the number of waves that moved past theperson is:A: 1 waveB: 3x108 wavesC: 1.5x108 wavesD: 6x108 wavesE: Not enough information21A radio wave of wavelength 2 meters passes by a person witha radio receiver. The person watches the E and B fields go upand down as the wave travels by. Later, a new radio wavepasses the person. They observe that the E and B fields go upand down 10 times faster than the original wave.What is the best conclusion? The second wave…A: has a wavelength of 0.2 mB: has a wavelength of 20 mC: travels 10 times faster.D: has 1/10 the frequency.E: More than one (or none of these) is
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