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Since current is directly proportional to voltage (Ohm’s law) and voltage is directly proportional to -field strength, the two should be directly proportional. It can be shown that the magnitudes of the fields do have a constant ratio, equal to the speed of light. That is,
is the ratio of -field strength to -field strength in any electromagnetic wave. This is true at all times and at all locations in space. A simple and elegant result.
What is the maximum strength of the -field in an electromagnetic wave that has a maximum -field strength of ?
Strategy
To find the -field strength, we rearrange the above equation to solve for , yielding
Solution
We are given , and is the speed of light. Entering these into the expression for yields
Where T stands for Tesla, a measure of magnetic field strength.
Discussion
The -field strength is less than a tenth of the Earth’s admittedly weak magnetic field. This means that a relatively strong electric field of 1000 V/m is accompanied by a relatively weak magnetic field. Note that as this wave spreads out, say with distance from an antenna, its field strengths become progressively weaker.
The result of this example is consistent with the statement made in the module Maxwell’s Equations: Electromagnetic Waves Predicted and Observed that changing electric fields create relatively weak magnetic fields. They can be detected in electromagnetic waves, however, by taking advantage of the phenomenon of resonance, as Hertz did. A system with the same natural frequency as the electromagnetic wave can be made to oscillate. All radio and TV receivers use this principle to pick up and then amplify weak electromagnetic waves, while rejecting all others not at their resonant frequency.
For your TV or radio at home, identify the antenna, and sketch its shape. If you don’t have cable, you might have an outdoor or indoor TV antenna. Estimate its size. If the TV signal is between 60 and 216 MHz for basic channels, then what is the wavelength of those EM waves?
Try tuning the radio and note the small range of frequencies at which a reasonable signal for that station is received. (This is easier with digital readout.) If you have a car with a radio and extendable antenna, note the quality of reception as the length of the antenna is changed.
Broadcast radio waves from KPhET. Wiggle the transmitter electron manually or have it oscillate automatically. Display the field as a curve or vectors. The strip chart shows the electron positions at the transmitter and at the receiver.
If an electromagnetic wave is described as having a frequency of 3 GHz, what are its period and wavelength (in a vacuum)?
(b)
Describe the outcome if you attempt to produce a longitudinal electromagnetic wave.
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