- Faraday's law
- Lenz's law
- Transformers
- Written Quiz Ch. 22 Chapter 25
- Electromagnetic radiation
- review Maxwell's equations
- electromagnetic waves applet
- Mechanical Universe video
- Lecture learning outcomes
A student who masters the topics in this lecture will be able to: - describe the basic features of an electromagnetic wave, including the speed of propagation and the relative orientations of the electric and magnetic fields
Try these additional examples
Example #2
Read textbook sections 25-2 through 25-4 before the next lecture
If the electric field in an electromagnetic wave is increasing in magnitude at a particular time, the magnitude of the magnetic field at the same time is _____.
A. increasing
B. decreasing
C. staying the same
Answer Walker5e 25.02
The electric field of an electromagnetic wave points in the positive y direction. At the same time, the magnetic field of this wave points in the positive z direction. In what direction is the wave traveling?
A. negative x direction
B. negative y direction
C. negative z direction
D. positive x direction
Answer
A. increasing The electric and magnetic fields are correlated to each other; when one increases, so does the other. Refer either to Figure 25-4 or to Equation 25-9, E = cB.
D. positive x direction Point the fingers of your right hand in the direction of E (positive y direction) and curl your fingers toward B (positive z direction), and your thumb points in the direction of propagation (positive x direction).
Suggest a new Definition
Proposed definitions will be considered for inclusion in the Economictimes.com
Definition: Electromagnetic waves or EM waves are waves that are created as a result of vibrations between an electric field and a magnetic field. In other words, EM waves are composed of oscillating magnetic and electric fields.
Description: Electromagnetic waves are formed when an electric field comes in contact with a magnetic field. They are hence known as ‘electromagnetic’ waves. The electric field and magnetic field of an electromagnetic wave are perpendicular (at right angles) to each other. They are also perpendicular to the direction of the EM wave.
EM waves travel with a constant velocity of 3.00 x 108 ms-1 in vacuum. They are deflected neither by the electric field, nor by the magnetic field. However, they are capable of showing interference or diffraction. An electromagnetic wave can travel through anything - be it air, a solid material or vacuum. It does not need a medium to propagate or travel from one place to another. Mechanical waves (like sound waves or water waves), on the other hand, need a medium to travel. EM waves are 'transverse' waves. This means that they are measured by their amplitude (height) and wavelength (distance between the highest/lowest points of two consecutive waves).
The highest point of a wave is known as 'crest', whereas the lowest point is known as 'trough'. Electromagnetic waves can be split into a range of frequencies. This is known as the electromagnetic spectrum. Examples of EM waves are radio waves, microwaves, infrared waves, X-rays, gamma rays, etc.
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Next: Effect of Dielectric Materials Up: Electromagnetic Waves Previous: Maxwell's Equations One of the first things that Maxwell did with his four equations, once he had obtained them, was to look for wave-like solutions. Maxwell knew that the wave-like solutions of the equations of gas dynamics correspond to sound waves, and the wave-like solutions of the equations of fluid dynamics correspond to gravity waves in water, so he reasoned that if his equations possessed wave-like solutions then these would correspond to a completely new type of wave, which he called an electromagnetic wave.
Maxwell was primarily interested in
electromagnetic waves which can propagate through a vacuum (i.e., a region containing no charges or currents). Now, in a vacuum, Maxwell's equations reduce to
where
Consider a plane electromagnetic wave propagating along the
Note that the fields are periodic in both time and space. The oscillation frequency (in hertz) of the fields at a given point in space is
(325) |
where
(326) |
Maxwell was able to establish that electromagnetic waves possess the following properties:
- The magnetic field oscillates in phase with the electric field. In other words, a wave maximum of the magnetic field always coincides with a wave maximum of the electric field in both time and space.
- The electric field is always perpendicular to the magnetic field, and both fields are directed at right-angles to the direction of propagation of the wave. In fact, the wave propagates in the direction . Electromagnetic waves are clearly a type of transverse wave.
- For a
-directed wave, the electric field is free to oscillate in any direction which lies in the-plane. The direction in which the electric field oscillates is conventionally termed the direction of polarization of the wave. Thus, Eqs. (323) represent a plane electromagnetic wave which propagates along the-axis, and is polarized in the-direction.
- The maximum amplitudes of the electric and the magnetic fields are related via
(327) - There is no constraint on the possible frequency or wavelength of electromagnetic waves. However, the propagation velocity of electromagnetic waves is fixed, and takes the value
(328)
According to Eqs. (321) and (322), a changing magnetic field generates an electric field, and a changing electric field generates a magnetic field. Thus, we can think of the propagation of an electromagnetic field through a vacuum as due to a kind of ``leap-frog'' effect, in which a changing electric field generates a magnetic field, which, in turn, generates an electric field, and so on. Note that the displacement current term in Eq. (322) plays a crucial role in the propagation of electromagnetic waves. Indeed, without this term, a changing electric field is incapable of generating a magnetic field, and so there can be no leap-frog effect. Electromagnetic waves have many properties in common with other types of wave (e.g., sound waves). However, they are unique in one respect: i.e., they are able to propagate through a vacuum. All other types of waves require some sort of medium through which to propagate.
Maxwell deduced that the speed of propagation of an electromagnetic wave through a vacuum is entirely determined by the constants
(329) |
Now, Maxwell knew [from the work of Fizeau (1849) and Foucault (1850)] that the velocity of light was about
Maxwell was able to make another remarkable prediction. The wavelength of light was well known in the late nineteenth century from studies of diffraction through slits, etc. Visible light actually occupies a surprisingly narrow range of wavelengths. The shortest wavelength blue light which is visible has a wavelength of
Since Maxwell's time, virtually all of the non-visible parts of the electromagnetic spectrum have been
observed. Table 3 gives a brief guide to the electromagnetic spectrum. Electromagnetic waves are of particular importance because they are our only source of information regarding the Universe around us. Radio waves and microwaves (which are comparatively hard to scatter) have provided much of our knowledge about the centre of the Galaxy. This is completely unobservable in visible light,
which is strongly scattered by interstellar gas and dust lying in the galactic plane. For the same reason, the spiral arms of the Galaxy can only be mapped out using radio waves. Infrared radiation is useful for detecting proto-stars which are not yet hot enough to emit visible radiation. Of course, visible radiation is still the mainstay of astronomy. Satellite based ultraviolet observations have yielded invaluable insights into the structure and distribution of distant galaxies. Finally, X-ray
and
Next: Effect of Dielectric Materials Up: Electromagnetic Waves Previous: Maxwell's Equations Richard Fitzpatrick 2007-07-14