Electromagnetic Waves Maxwell’s Equations

“Sourceless” Maxwell’s Equations

... need to verify consistency with Maxwell’s Equations A simple Electromagnetic Wave Pulse: E and B constant within a “sheet” moving at velocity v x y E B v z ... need to verify consistency with Maxwell’s Equations

Field lines continue forever: each field line which enters (exits) a closed surface must also enter (exit), so net number of field lines entering (exiting) a closed surface must be zero.

dA dl L v dt

dl L dA v dt

General relations between (crossed) E and B fields creating EM waves. x y a x

x y a x

Classical Wave Equation!

Sinusoidal Electromagnetic Waves Ey Bz x

Energy in an electromagnetic wave

Energy in an electromagnetic wave

Energy Flow and Harmonic Waves

Example: A radio station the surface of the earth emits 50 kW sinusoidal waves. Determine the intensity, and the Electric and Magnetic field amplitudes for an orbiting satellite at a distance of 100 km from the station.

Momentum in an electromagnetic wave

Example: Satellite in previous example has a 2m diameter antenna Example: Satellite in previous example has a 2m diameter antenna. What is the force of the radiation on the antenna assuming perfect reflection?

Standing Waves: Superposition of equal amplitude traveling waves of opposite directions.

Example: EM standing waves are set up in a cavity used for electron spin resonance studies. The cavity has two parallel conducting plates separated by 1.50 cm. a) Calculate the longest wavelength and lowest frequency of EM standing waves between the walls. b) Where in the cavity is the maximum magnitude electric field and magnetic field?

Electromagnetic Spectrum (see graphic) in vacuum, v = c = 2.99792458x108 m/s f = v increasing frequency <=> decreasing wavelength visible spectrum: 400 nm (violet) to 700 nm (red)

Radiation from a Dipole Q Q