# electromagnetic waves hertz’s discoveries plane electromagnetic waves energy in an em wave...

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• Electromagnetic WavesHertzs DiscoveriesPlane Electromagnetic WavesEnergy in an EM WaveMomentum and Radiation PressureThe Electromagnetic Spectrum

• Maxwell: Problem with Ampres LawAmpres LawFor S1,For S2,(No current in the gap)But there is a problem!Consider a parallel plate capacitor

• Contradiction!What can we do to fix it?Amperes Law works well most of the time.What is special about the region between the capacitors?Lets try to relate E to the current I.

Try fudging Amperes Law:

• Solution - Displacement CurrentCall I as the conduction current.Specify a new current that exists when a change in the electric field occurs. Call it the displacement current.Electrical flux through S2:

• Maxwell Gets Excited!Free Space: I = 0, Q = 0

• WavesCircular (or Spherical in 3D) WavesPlane Waves

• Ampre-Maxwell LawMagnetic fields are produced by both conduction currents and by time-varying electrical fields.Now the generalized form of Ampres Law, or Ampre-Maxwell Lax becomes:

• Maxwells Equations

• Hertzs Radio WavesBy supplying short voltage bursts from the coil to the transmitter electrode we can ionize the air between the electrodes.In effect, the circuit can be modeled as a LC circuit, with the coil as the inductor and the electrodes as the capacitor.A receiver loop placed nearby is able to receive these oscillations and creates sparks as well.

• EM Wave Oscillation

• Some Important Quantities

• Properties of EM WavesThe solutions to Maxwells equations in free space are wavelikeElectromagnetic waves travel through free space at the speed of light.The electric and magnetic fields of a plane wave are perpendicular to each other and the direction of propagation (they are transverse).The ratio of the magnitudes of the electric and magnetic fields is c.EM waves obey the superposition principle.

• An EM Wavea) l=?, T=?b) If Emax=750N/C, then Bmax=?Directed towards the z-directionc) E(t)=? and B(t)=?

• Energy Carried by EM WavesPoynting Vector (W/m2)For a plane EM Wave:The average value of S is called the intensity:S is equal to the rate of EM energy flow per unit area (power per unit area)

• The Energy DensityFor an EM wave, the instantaneous electric and magnetic energies are equal.Total Energy Density of an EM WaveThe intensity is c times the total average energy density

• Concept QuestionWhich gives the largest average energy densityat the distance specified and thus, at least qualitatively, the best illumination

1. a 50-W source at a distance R.2. a 100-W source at a distance 2R.3. a 200-W source at a distance 4R.

• Fields on the ScreenP lamp= 150 W, 3% efficiencyA = 15 m2

• Momentum and Radiation PressureMomentum for complete absorptionPressure on surfaceFor complete reflection:

• Pressure From a Laser PointerP laser= 3 mW, 70% reflection, d = 2 mm

• Review of key points:Partial derivativesRelationship between E and BPoynting vectorOmit section 34.4.Section 34.5: only responsible for ideas presented next.

• Properties of EM WavesThe solutions to Maxwells equations in free space are wavelikeElectromagnetic waves travel through free space at the speed of light.The electric and magnetic fields of a plane wave are perpendicular to each other and the direction of propagation (they are transverse).The ratio of the magnitudes of the electric and magnetic fields is c.EM waves obey the superposition principle.

• Energy Carried by EM WavesPoynting Vector (W/m2)For a plane EM Wave:The average value of S is called the intensity:S is equal to the rate of EM energy flow per unit area (power per unit area)

• AntennasThe fundamental mechanism for electromagnetic radiation is an accelerating charge

• Half-Wave Antenna