1. Energy in EM Waves: The Poynting Vector

2. Energy in The Electric Field: from Chapter 18
The energy per unit volume (energy
density) in the Electric Field is:
u =

3. Energy in The Magnetic Field: from Chapter 20
The energy per unit volume (energy
density) in the Magnetic Field is:
u =

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

5. This energy is transported by the wave.
Figure Electromagnetic wave carrying energy through area A.
This energy is transported by the wave.

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

7. Example: E & 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.
Solution: The rate at which radiation arrives is the average value of S; we can use equation 31-19a to find E0 and B0.
E0 = 1.01 x 103 V/m.
B0 = 3.37 x 10-6 T.

8. 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:

9. 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.
Solution: Estimate P = S/c = 3 x 10-6 N/m2. If your hand is about 10 cm by 20 cm, or 0.02 m2, this translates to a force of 6 x 10-8 N.

10. 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, &
(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?
Solution: Estimate P = S/c = 3 x 10-6 N/m2. If your hand is about 10 cm by 20 cm, or 0.02 m2, this translates to a force of 6 x 10-8 N.

11. 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.
Figure Block diagram of a radio transmitter.

12. The mixing of signal and carrier can be done two ways
The mixing of signal and carrier can be done two ways. First, by using the signal to modify the amplitude of the carrier (AM):
Figure In amplitude modulation (AM), the amplitude of the carrier signal is made to vary in proportion to the audio signal’s amplitude.

13. Second, by using the signal to modify the frequency of the carrier (FM):
Figure In frequency modulation (FM), the frequency of the carrier signal is made to change in proportion to the audio signal’s amplitude. This method is used by FM radio and television.

14. At the receiving end, the wave is received, demodulated, amplified, & sent to a loudspeaker.
The receiving antenna is bathed in waves of many frequencies; a tuner is used to select the desired one.
Figure Block diagram of a simple radio receiver.

15. Example: Tuning a Station.
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.
Figure Antennas. (a) Electric field of EM wave produces a current in an antenna consisting of straight wire or rods. (b) Changing magnetic field induces an emf and current in a loop antenna.

16. Summary Maxwell’s Equations
B(2r) = EA
These are the
basic equations of
electromagnetism:
B(2r) = BA
B(2r) =
B Eℓ t
E
B(2r) t