Transcript E&M Waves
Chapter 21 Electromagnetic Waves Exam II Curve: +30 General Physics Electromagnetic Waves Ch 21, Secs 8–12 General Physics James Clerk Maxwell 1831 – 1879 Electricity and magnetism were originally thought to be unrelated In 1865, James Clerk Maxwell provided a mathematical theory that showed a close relationship between all electric and magnetic phenomena Electromagnetic theory of light General Physics Maxwell’s Starting Points Electric field lines originate on positive charges and terminate on negative charges Magnetic field lines always form closed loops – they do not begin or end anywhere General Physics Can electric fields form closed loops? 1. 2. Yes No 50% 1 2 3 4 5 6 7 8 21 22 23 24 25 26 27 28 9 10 11 12 13 14 10 50% 15 1 29 30 General Physics 16 17 18 2 19 20 Maxwell’s Starting Points A varying magnetic field induces an emf and hence an electric field (Faraday’s Law) Magnetic fields are generated by moving charges or currents (Ampère’s Law) General Physics Maxwell’s Hypothesis Turning Faraday’s Law upside down, Maxwell hypothesized that a changing electric field would produce a magnetic field (Maxwell-Ampère’s Law) General Physics Maxwell Equations closed surface enclosed charge closed loop • Conservation of energy closed surface closed loop linked flux no mag. charge linked current + flux • Conservation of charge Lorentz force law General Physics Maxwell’s Predictions Maxwell concluded that visible light and all other electromagnetic (EM) waves consist of fluctuating electric and magnetic fields, with each varying field inducing the other Accelerating charges generate these time varying E and B fields Maxwell calculated the speed at which these electromagnetic waves travel in a vacuum – speed of light c = 3.00 x 108 m/s General Physics Hertz’s Confirmation of Maxwell’s Predictions 1857 – 1894 First to generate and detect electromagnetic waves in a laboratory setting Showed radio waves could be reflected, refracted and diffracted The unit Hz is named for him General Physics Hertz’s Experimental Apparatus An induction coil is connected to two large spheres forming a capacitor Oscillations are initiated by short voltage pulses The oscillating current (accelerating charges) generates EM waves General Physics Hertz’s Experiment Several meters away from the transmitter is the receiver This consisted of a single loop of wire connected to two spheres When the oscillation frequency of the transmitter and receiver matched, energy transfer occurred between them General Physics Hertz’s Conclusions Hertz hypothesized the energy transfer was in the form of waves These are now known to be electromagnetic waves Hertz confirmed Maxwell’s theory by showing the waves existed and had all the properties of light waves (e.g., reflection, refraction, diffraction) They had different frequencies and wavelengths which obeyed the relationship v = f λ for waves v was very close to 3 x 108 m/s, the known speed of light General Physics EM Waves by an Antenna Two rods are connected to an oscillating source, charges oscillate between the rods (a) As oscillations continue, the rods become less charged, the field near the charges decreases and the field produced at t = 0 moves away from the rod (b) The charges and field reverse (c) – the oscillations continue (d) General Physics EM Waves by an Antenna, final Because the oscillating charges in the rod produce a current, there is also a magnetic field generated As the current changes, the magnetic field spreads out from the antenna The magnetic field is perpendicular to the electric field General Physics Electromagnetic Waves, Summary A changing magnetic field produces an electric field A changing electric field produces a magnetic field These fields are in phase At any point, both fields reach their maximum value at the same time General Physics Electromagnetic Waves are Transverse Waves The E and B fields are perpendicular to each other Both fields are perpendicular to the direction of motion Therefore, EM waves are transverse waves Active Figure: A Transverse Electromagnetic Wave General Physics Properties of EM Waves Electromagnetic waves are transverse waves They travel at the speed of light c 1 o o This supports the fact that light is an EM wave General Physics Properties of EM Waves, 2 The ratio of the electric field to the magnetic field is equal to the speed of light E Emax c B Bmax Electromagnetic waves carry energy as they travel through space, and this energy can be transferred to objects placed in their path General Physics Properties of EM Waves, 3 Energy carried by EM waves is shared equally by the electric and magnetic fields Average power per unit area 2 max 2 max Pave Emax Bmax E cB I A 20 20c 20 General Physics Properties of EM Waves, final Electromagnetic waves transport linear momentum as well as energy For complete absorption of energy U p = U/c F = Pave/c For complete reflection of energy U p = (2U)/c F = 2Pave/c Radiation pressures (forces) can be determined experimentally General Physics Determining Radiation Pressure This is an apparatus for measuring radiation pressure In practice, the system is contained in a vacuum The pressure is determined by the angle at which equilibrium occurs General Physics Summary of Properties of Electromagnetic (EM) Waves They travel at the speed of light They are transverse waves Ratio of E and B field magnitudes: E/B=c E, B perpendicular to each other and velocity Electric and magnetic fields carry equal energy They carry both energy and momentum Can deliver U and p to a surface General Physics The Spectrum of EM Waves Forms of electromagnetic waves exist that are distinguished by their frequency and wavelength c = ƒλ Wavelengths for visible light range from 400–700 nm a small portion of the spectrum Wavelengths 1 1 1 1 1 km = 10-3 m (radio) electronic m = 10-6 m (visible, IR) nm = 10-9 m (UV, X-ray) Å = 10-10 m (X-ray) atomic fm =10-15 m (-ray) nuclear General Physics