Chapter 21 Electromagnetic Waves

General Physics 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 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 In 1865, James Clerk Maxwell provided a mathematical theory that showed a close relationship between all electric and magnetic phenomena Electromagnetic theory of light Electromagnetic theory of light

General Physics Maxwell’s Starting Points Electric field lines originate on positive charges and terminate on negative charges 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 Magnetic field lines always form closed loops – they do not begin or end anywhere

General Physics Can electric fields form closed loops? 1. Yes 2. No

General Physics Maxwell’s Starting Points Magnetic fields are generated by moving charges or currents (Ampère’s Law) Magnetic fields are generated by moving charges or currents (Ampère’s Law) A varying magnetic field induces an emf and hence an electric field (Faraday’s Law) A varying magnetic field induces an emf and hence an electric field (Faraday’s Law)

General Physics Turning Faraday’s Law upside down, Maxwell hypothesized that a changing electric field would produce a magnetic field (Maxwell-Ampère’s Law) Turning Faraday’s Law upside down, Maxwell hypothesized that a changing electric field would produce a magnetic field (Maxwell-Ampère’s Law) Maxwell’s Hypothesis

General Physics Maxwell Equations closed surface enclosed charge closed surface no mag. charge Conservation of energy closed loop linked current + flux Conservation of charge Lorentz force law closed loop linked flux

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 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 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 10 8 m/s Maxwell calculated the speed at which these electromagnetic waves travel in a vacuum – speed of light c = 3.00 x 10 8 m/s

General Physics Hertz’s Confirmation of Maxwell’s Predictions 1857 – – 1894 First to generate and detect electromagnetic waves in a laboratory setting First to generate and detect electromagnetic waves in a laboratory setting Showed radio waves could be reflected, refracted and diffracted Showed radio waves could be reflected, refracted and diffracted The unit Hz is named for him 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 An induction coil is connected to two large spheres forming a capacitor Oscillations are initiated by short voltage pulses Oscillations are initiated by short voltage pulses The oscillating current (accelerating charges) generates EM waves The oscillating current (accelerating charges) generates EM waves

General Physics Hertz’s Experiment Several meters away from the transmitter is the receiver Several meters away from the transmitter is the receiver This consisted of a single loop of wire connected to two spheres 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 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 Hertz hypothesized the energy transfer was in the form of waves These are now known to be electromagnetic 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) 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 They had different frequencies and wavelengths which obeyed the relationship v = f λ for waves v was very close to 3 x 10 8 m/s, the known speed of light v was very close to 3 x 10 8 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) 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) 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) 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 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 As the current changes, the magnetic field spreads out from the antenna The magnetic field is perpendicular to the electric field The magnetic field is perpendicular to the electric field

General Physics Electromagnetic Waves, Summary A changing magnetic field produces an electric field A changing magnetic field produces an electric field A changing electric field produces a magnetic field A changing electric field produces a magnetic field These fields are in phase These fields are in phase At any point, both fields reach their maximum value at the same time At any point, both fields reach their maximum value at the same time

General Physics Electromagnetic Waves are Transverse Waves The and fields are perpendicular to each other The and fields are perpendicular to each other Both fields are perpendicular to the direction of motion Both fields are perpendicular to the direction of motion Therefore, EM waves are transverse waves Therefore, EM waves are transverse waves Active Figure: A Transverse Electromagnetic WaveA Transverse Electromagnetic Wave

General Physics Properties of EM Waves Electromagnetic waves are transverse waves Electromagnetic waves are transverse waves They travel at the speed of light They travel at the speed of light This supports the fact that light is an EM wave 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 The ratio of the electric field to the magnetic field is equal to the speed of light Electromagnetic waves carry energy as they travel through space, and this energy can be transferred to objects placed in their path 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 Energy carried by EM waves is shared equally by the electric and magnetic fields Average power per unit area Average power per unit area

General Physics Properties of EM Waves, final Electromagnetic waves transport linear momentum as well as energy Electromagnetic waves transport linear momentum as well as energy For complete absorption of energy U For complete absorption of energy U p = U/c  F = P ave /c For complete reflection of energy U For complete reflection of energy U p = (2U)/c  F = 2P ave /c Radiation pressures (forces) can be determined experimentally Radiation pressures (forces) can be determined experimentally

General Physics Determining Radiation Pressure This is an apparatus for measuring radiation pressure This is an apparatus for measuring radiation pressure In practice, the system is contained in a vacuum In practice, the system is contained in a vacuum The pressure is determined by the angle at which equilibrium occurs 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 travel at the speed of light They are transverse waves They are transverse waves E, B perpendicular to each other and velocity E, B perpendicular to each other and velocity Ratio of E and B field magnitudes: E/B=c Ratio of E and B field magnitudes: E/B=c Electric and magnetic fields carry equal energy Electric and magnetic fields carry equal energy They carry both energy and momentum They carry both energy and momentum Can deliver U and p to a surface 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 Forms of electromagnetic waves exist that are distinguished by their frequency and wavelength c = ƒλ c = ƒλ Wavelengths for visible light range from 400–700 nm Wavelengths for visible light range from 400–700 nm a small portion of the spectrum a small portion of the spectrum Wavelengths Wavelengths 1 km = m (radio) electronic 1 km = m (radio) electronic 1  m = m (visible, IR) 1  m = m (visible, IR) 1 nm = m (UV, X-ray) 1 nm = m (UV, X-ray) 1 Å = m (X-ray) atomic 1 Å = m (X-ray) atomic 1 fm = m (  -ray) nuclear 1 fm = m (  -ray) nuclear