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Energy in EM Waves: The Poynting Vector

Energy in EM Waves: The Poynting Vector. Energy in EM Waves: The Poynting Vector. Energy is stored in both electric & magnetic fields, giving the total energy density of an electromagnetic wave:. Each field contributes half the total energy density:. This energy is transported by the wave.

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Energy in EM Waves: The Poynting Vector

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  1. Energy in EM Waves: The Poynting Vector

  2. Energy in EM Waves:The Poynting Vector Energy is stored in both electric & magnetic fields, giving the total energy density of an electromagnetic wave: Each field contributes half the total energy density:

  3. This energy is transported by the wave.

  4. . The energy transported through a unit area per unit time is called the intensity: Its vector form is the Poynting vector: Typically we are interested in the time average value of S:

  5. Example: E and B from the Sun. Radiation from the Sun reaches the Earth (above the atmosphere) at a rate of about 1350 J/s·m2 (= 1350 W/m2). Assume that this is a single EM wave, and calculate the maximum values of E and B.

  6. Radiation Pressure In addition to carrying energy, electromagnetic waves also carry momentum. This means that a force will be exerted by the wave. The radiation pressure is related to the average intensity. It is a minimum if the wave is fully absorbed: and a maximum if it is fully reflected:

  7. Example: Solar pressure. Radiation from the Sun that reaches the Earth’s surface (after passing through the atmosphere) transports energy at a rate of about 1000 W/m2. Estimate the pressure and force exerted by the Sun on your outstretched hand. Example: A solar sail. Proposals have been made to use the radiation pressure from the Sun to help propel spacecraft around the solar system. (a) About how much force would be applied on a 1 km x 1 km highly reflective sail, and (b) by how much would this increase the speed of a 5000-kg spacecraft in one year? (c) If the spacecraft started from rest, about how far would it travel in a year?

  8. Radio and Television; Wireless Communication This figure illustrates the process by which a radio station transmits information. The audio signal is combined with a carrier wave.

  9. The mixing of signal and carrier can be done two ways. First, by using the signal to modify the amplitude of the carrier (AM):

  10. Second, by using the signal to modify the frequency of the carrier (FM):

  11. At the receiving end, the wave is received, demodulated, amplified, and sent to a loudspeaker. The receiving antenna is bathed in waves of many frequencies; a tuner is used to select the desired one.

  12. A straight antenna will have a current induced in it by the varying electric fields of a radio wave; a circular antenna will have a current induced by the changing magnetic flux. Example: Tuning a station. Calculate the transmitting wavelength of an FM radio station that transmits at 100 MHz.

  13. Summary of Chapter • Maxwell’s Equations are the basic equations of electromagnetism:

  14. Electromagnetic waves are produced by accelerating • charges; the propagation speed is given by • The wavelength and frequency of EM waves are related: • The fields are perpendicular to each other and to the direction of propagation. • The electromagnetic spectrum includes all wavelengths, from radio waves through visible light to gamma rays. • The Poynting vector describes the energy carried by EM waves:

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