1. Four equations (integral form) : Gauss’s law Gauss’s law for magnetism Faraday’s law Ampere-Maxwell law + Lorentz force Maxwell’s Equations

2. Time varying magnetic field makes electric field Time varying electric field makes magnetic field Fields Without Charges

3. Key idea: Fields travel in space at certain speed Disturbance moving in space – a wave? 1. Simplest case: a pulse (moving slab) A Simple Configuration of Traveling Fields

4. E=Bv Based on Maxwell’s equations, pulse must propagate at speed of light E=cB A Pulse: Speed of Propagation

5. Electromagnetic pulse can propagate in space How can we initiate such a pulse? Short pulse of transverse electric field Accelerated Charges

6. 1.Transverse pulse propagates at speed of light 2.Since E(t) there must be B 3.Direction of v is given by: E B v Accelerated Charges

7. We can qualitatively predict the direction. What is the magnitude? Magnitude can be derived from Gauss’s law Field ~ -qa  1. The direction of the field is opposite to qa  2. The electric field falls off at a rate 1/r Magnitude of the Transverse Electric Field

8. Field of an accelerated charge 1 2 3 4 vT A B Accelerates for t, then coasts for T at v=at to reach B. cT ct No charge

9. Field of an accelerated charge 1 2 3 4 vT A B cT ct

10. Plane Electromagnetic Waves A plane wave consists of electric and magnetic fields that vary in space only in the direction of the wave propagation. –The fields are perpendicular to each other and to the direction of propagation.

11. Positive Charge in EM wave

12. A particle will experience electric force during a short time d/c: What will happen to the ball? It will oscillate Energy was transferred from E/M field to the ball Amount of energy in the pulse is ~ E 2 Energy of E/M Radiation

13. Ball gained energy: Pulse energy must decrease E/M radiation: E=cB Energy of E/M Radiation

14. There is E/M energy stored in the pulse: Pulse moves in space: there is energy flux Units: J/(m 2 s) = W/m 2 During  t: used: E=cB,  0  0 =1/c 2 Energy Flux

15. The direction of the E/M radiation was given byEnergy flux, the “Poynting vector”: S is the rate of energy flux in E/M radiation It points in the direction of the E/M radiation John Henry Poynting (1852-1914) Energy Flux: The Poynting Vector

16. In the vicinity of the Earth, the energy density of radiation emitted by the sun is ~1400 W/m 2. What is the approximate magnitude of the electric field in the sunlight? Solution: Note: this is an average (rms) value Exercise

17. A laser pointer emits ~5 mW of light power. What is the approximate magnitude of the electric field? Solution: 1.Spot size: ~2 mm 2.flux = (5. 10 -3 W)/(3.14. 0.001 2 m 2 )=1592 W/m 2 3.Electric field: (rms value) What if we focus it into 2 a micron spot? Flux will increase 10 6 times, E will increase 10 3 times: Exercise

18. E field starts motion Moving charge in magnetic field: F mag What if there is negative charge? F mag ‘Radiation pressure’: What is its magnitude? Average speed: v/2 Momentum of E/M Radiation

19. Net momentum: in transverse direction: 0 in longitudinal direction: >0 Relativistic energy: Quantum view: light consists of photons with zero mass: Classical (Maxwell): it is also valid, i.e. momentum = energy/speed Momentum flux: Momentum Flux Units of Pressure

20. Solution: If reflective surface? Total force on the sail: Exercise: Solar Sail Atmospheric pressure is ~ 10 5 N/m 2

21. Electric fields are not blocked by matter: how can E decrease? Re-radiation: Scattering Positive charge

22. Electromagnetic Spectrum

23. Need to create oscillating motion of electrons Radio frequency LC circuit: can produce oscillating motion of charges To increase effect: connect to antenna Visible light Heat up atoms, atomic vibration can reach visible frequency range Transitions of electrons between different quantized levels E/M Radiation Transmitters How can we produce electromagnetic radiation of a desired frequency?

24. AC voltage (~300 MHz) What will happen if distance is increased twice? no light E/M radiation can be polarized along one axis… …and it can be unpolarized: Polarized E/M Radiation

25. Making polarized lightTurning polarization Polaroid sunglasses and camera filters: reflected light is highly polarized: can block it Considered: using polarized car lights and polarizers-windshields Polarized Light

26. In which of these situations will the bulb light? A)A B)B C)C D)None E)B and C

27. Why there is light coming from the sky? Why is it polarized? Why is it blue? Energy flux: Ratio of blue/red frequency is ~2  scattering intensity ratio is 16 Why is sun red at sunset? Is its light polarized? Why the Sky is Blue

28. Why there is no light going through a cardboard? Electric fields are not blocked by matter Electrons and nucleus in cardboard reradiate light Behind the cardboard reradiated E/M field cancels original field Cardboard

29. 1.Radiative pressure – too small to be observed in most cases 2.E/M fields can affect charged particles: nucleus and electrons Both fields (E and M) are always present – they ‘feed’ each other But usually only electric field is considered (B=E/c) Effect of E/M Radiation on Matter

30. Effect of Radiation on a Neutral Atom Main effect: brief electric kick sideways Neutral atom: polarizes Electron is much lighter than nucleus: can model atom as outer electron connected to the rest of the atom by a spring: F=eE ResonanceSee 15.P.47

31. Radiation and Neutral Atom: Resonance Amplitude of oscillation will depend on how close we are to the natural free-oscillation frequency of the ball- spring system Resonance

32. E/M radiation waves with frequency ~10 6 Hz has big effect on mobile electrons in the metal of radio antenna: can tune radio to a single frequency E/M radiation with frequency ~ 10 15 Hz has big effect on organic molecules: retina in your eye responds to visible light but not radio waves Very high frequency (X-rays) has little effect on atoms and can pass through matter (your body): X-ray imaging Importance of Resonance