1. Electromagnetic waves
Physics 114
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2. Concepts EM waves – frequency and wave length EM spectrum Antennas
Radio
Amplitude and frequency modulations
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3. Maxwell’s equations in vacuum
No charges, no currents
Changing magnetic field creates electric field
Changing electric field creates magnetic field
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4. EM wave
The speed of light!!
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5. EM spectrum c – speed of light (m/s) f – frequency (Hz=1/s)
l – wavelength (m)
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6. Waves Propagating oscillation = wave.
Waves transport energy and information, but do not transport matter.
Examples:
Ocean waves
Sound
Light
Radio waves
Matter
Wave
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7. 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
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8. 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
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9. 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
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10. 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
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11. 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
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12. 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:
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13. 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:
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14. 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
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15. 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)
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16. Modulations Amplitude modulation (AM) Frequency modulation (FM)
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17. 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.
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18. Constructive and destructive interference
in phase out of phase not in phase
Constructive Destructive Partially destructive A 2A
<A
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