Electromagnetic waves Physics 114 11/27/2018 Lecture X

Concepts EM waves – frequency and wave length EM spectrum Antennas Radio Amplitude and frequency modulations 11/27/2018 Lecture X

Maxwell’s equations in vacuum No charges, no currents Changing magnetic field creates electric field Changing electric field creates magnetic field 11/27/2018 Lecture X

EM wave The speed of light!! 11/27/2018 Lecture X

EM spectrum c – speed of light (m/s) f – frequency (Hz=1/s) l – wavelength (m) 11/27/2018 Lecture X

Waves Propagating oscillation = wave. Waves transport energy and information, but do not transport matter. Examples: Ocean waves Sound Light Radio waves Matter Wave 11/27/2018 Lecture X

Waves Wave velocity: Wavelength – l v=l/T=lf Period T Frequency f=1/T The only equation that you need to remember about waves. Wave velocity is NOT the same as particle velocity of the medium Wavelength – l Period T Frequency f=1/T 11/27/2018 Lecture X

Transverse and longitudinal waves In transverse wave the velocity of particles of the medium is perpendicular to the velocity of wave. In EM wave electric field is perpendicular to the wave velocity and so is the magnetic field. Thus EM wave is a transverse wave. Wave Matter 11/27/2018 Lecture X

Transverse and longitudinal waves In longitudinal wave the velocity of particles of the medium is parallel (or anti-parallel) to the wave velocity. Example of longitudinal wave is sound. Wave Matter 11/27/2018 Lecture X

Description of waves w=2pf – cyclic frequency, k=2p/l –wave vector D=D0sin(kx-wt+d), d-phase at t=0, x=0 Riding the wave kx-wt+d=const kx-wt=c x=c/k+(w/k)t = x0+vt Thus, wave velocity v=w/k=2pf/ (2p/l)=fl = l/T D=D0sin(kx-wt) – wave is moving in +x direction D=D0sin(kx+wt) – wave is moving in -x direction 11/27/2018 Lecture X

Energy in EM wave EM waves transport energy Energy density: Poynting vector (energy transported by EM wave per unit time per unit area) Average energy per unit time per unit area 11/27/2018 Lecture X

Average intensity Displacement D follows harmonic oscillation: Intensity (brightness for light) I is proportional to electric field squared Average over time (one period of oscillation) I: 11/27/2018 Lecture X

Energy transported by waves Intensity of oscillation I (energy per unit area/ per sec) is proportional to amplitude squared D2 3D wave (from energy conservation): D12 4pr12= D22 4pr22 D1/D2=r2/r1 Amplitude of the wave is inversely proportional to the distance to the source: 11/27/2018 Lecture X

Radiation from an AC antenna Changing electric field creates magnetic field Changing magnetic field creates electric field Change propagates with a finite velocity Electromagnetic wave – proof of unification 11/27/2018 Lecture X

Transmission and reception Antennas are used to transmit and to receive EM waves Rod antennas – transmit and receive E component E || to rod Loop antennas – B component (use induction) 11/27/2018 Lecture X

Modulations Amplitude modulation (AM) Frequency modulation (FM) 11/27/2018 Lecture X

Interference of waves When two or more waves pass through the same region of space, we say that they interfere. Principle of superposition (fancy word for sum of waves): the resultant displacement is the algebraic sum of individual displacements created by these waves. 11/27/2018 Lecture X

Constructive and destructive interference in phase out of phase not in phase Constructive Destructive Partially destructive A 2A <A 11/27/2018 Lecture X