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

Acceleration: Sinusoidal E/M field Sinusoidal Electromagnetic Radiation

Sinusoidal E/M Radiation: Wavelength Freeze picture in time: Instead of period can use wavelength: Example of sinusoidal E/M radiation: atoms radio stations E/M noise from AC wires

According to particle theory of light: photons have energy and momentum Classical E/M model of light: E/M radiation must carry energy and momentum Energy and Momentum of E/M Radiation

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

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

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

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 ( ) Energy Flux: The Poynting Vector

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

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 = ( W)/( 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

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

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

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

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

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

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

In transparent media, the superposition can result in change of wavelength and speed of wavefront Refraction: Bending of Light Rays perpendicular to wavefront bend at surface

A ray bends as it goes from one transparent media to another Refraction: Snell’s Law

Reflection and transmission Total Internal Reflection