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8.2 Production of electromagnetic waves  (Page 3/14)

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Relating E size 12{E} {} -field and B size 12{B} {} -field strengths

There is a relationship between the E size 12{E} {} - and B size 12{B} {} -field strengths in an electromagnetic wave. This can be understood by again considering the antenna just described. The stronger the E size 12{E} {} -field created by a separation of charge, the greater the current and, hence, the greater the B size 12{B} {} -field created.

Since current is directly proportional to voltage (Ohm’s law) and voltage is directly proportional to E size 12{E} {} -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,

E B = c size 12{ { {E} over {B} } =c} {}

is the ratio of E size 12{E} {} -field strength to B size 12{B} {} -field strength in any electromagnetic wave. This is true at all times and at all locations in space. A simple and elegant result.

Calculating B size 12{B} {} -field strength in an electromagnetic wave

What is the maximum strength of the B size 12{B} {} -field in an electromagnetic wave that has a maximum E size 12{E} {} -field strength of 1000 V/m size 12{"1000" {V} slash {m} } {} ?

Strategy

To find the B size 12{B} {} -field strength, we rearrange the above equation to solve for B size 12{B} {} , yielding

B = E c . size 12{B= { {E} over {c} } } {}

Solution

We are given E size 12{E} {} , and c size 12{c} {} is the speed of light. Entering these into the expression for B size 12{B} {} yields

B = 1000 V/m 3 . 00 × 10 8 m/s = 3 . 33 × 10 - 6 T , size 12{B = { {"1000 V/m"} over {3 "." "00 " times " 10" rSup { size 8{8} } " m/s"} } =" 3" "." "33" times "10" rSup { size 8{ +- 6} } " T"} {}

Where T stands for Tesla, a measure of magnetic field strength.

Discussion

The B size 12{B} {} -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.

Take-home experiment: antennas

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.

Phet explorations: radio waves and electromagnetic fields

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.

Radio Waves and Electromagnetic Fields

Section summary

  • Electromagnetic waves are created by oscillating charges (which radiate whenever accelerated) and have the same frequency as the oscillation.
  • Since the electric and magnetic fields in most electromagnetic waves are perpendicular to the direction in which the wave moves, it is ordinarily a transverse wave.
  • The strengths of the electric and magnetic parts of the wave are related by
    E B = c , size 12{ { {E} over {B} } = ital " c"} {}

    which implies that the magnetic field B size 12{B} {} is very weak relative to the electric field E size 12{E} {} .

Conceptual questions

The direction of the electric field shown in each part of [link] is that produced by the charge distribution in the wire. Justify the direction shown in each part, using the Coulomb force law and the definition of E = F / q size 12{E= {F} slash {q} } {} , where q size 12{q} {} is a positive test charge.

Is the direction of the magnetic field shown in [link] (a) consistent with the right-hand rule for current (RHR-2) in the direction shown in the figure?

Why is the direction of the current shown in each part of [link] opposite to the electric field produced by the wire’s charge separation?

In which situation shown in [link] will the electromagnetic wave be more successful in inducing a current in the wire? Explain.

Part a of the diagram shows an electromagnetic wave approaching a long straight vertical wire. The wave is shown with the variation of two components E and B. E is a sine wave in vertical plane with small arrows showing the vibrations of particles in the plane. B is a sine wave in a horizontal plane perpendicular to the E wave. The B wave has arrows to show the vibrations of particles in the plane. The waves are shown intersecting each other at the junction of the planes because E and B are perpendicular to each other. The direction of propagation of wave is shown perpendicular to E and B waves. Part b of the diagram shows an electromagnetic wave approaching a long straight vertical wire. The wave is shown with the variation of two components E and B. E is a sine wave in horizontal plane with small arrows showing the vibrations of particles in the plane. B is a sine wave in a vertical plane perpendicular to the E wave. The B wave has arrows to show the vibrations of particles in the plane. The waves are shown intersecting each other at the junction of the planes because E and B are perpendicular to each other. The direction of propagation of wave is shown perpendicular to E and B waves.
Electromagnetic waves approaching long straight wires.

In which situation shown in [link] will the electromagnetic wave be more successful in inducing a current in the loop? Explain.

Part a of the diagram shows an electromagnetic wave approaching a receiver loop connected to a tuner. The wave is shown with the variation of two components E and B. E is a sine wave in vertical plane with small arrows showing the vibrations of particles in the plane. B is a sine wave in a horizontal plane perpendicular to the E wave. The B wave has arrows to show the vibrations of particles in the plane. The waves are shown intersecting each other at the junction of the planes because E and B are perpendicular to each other. The direction of propagation of wave is shown perpendicular to E and B waves. Part b of the diagram shows an electromagnetic wave approaching a receiver loop connected to a tuner. The wave is shown with the variation of two components E and B. E is a sine wave in horizontal plane with small arrows showing the vibrations of particles in the plane. B is a sine wave in a vertical plane perpendicular to the E wave. The B wave has arrows to show the vibrations of particles in the plane. The waves are shown intersecting each other at the junction of the planes because E and B are perpendicular to each other. The direction of propagation of wave is shown perpendicular to E and B waves.
Electromagnetic waves approaching a wire loop.

Should the straight wire antenna of a radio be vertical or horizontal to best receive radio waves broadcast by a vertical transmitter antenna? How should a loop antenna be aligned to best receive the signals? (Note that the direction of the loop that produces the best reception can be used to determine the location of the source. It is used for that purpose in tracking tagged animals in nature studies, for example.)

Under what conditions might wires in a DC circuit emit electromagnetic waves?

Give an example of interference of electromagnetic waves.

[link] shows the interference pattern of two radio antennas broadcasting the same signal. Explain how this is analogous to the interference pattern for sound produced by two speakers. Could this be used to make a directional antenna system that broadcasts preferentially in certain directions? Explain.

The picture shows an overhead view of a radio broadcast antenna sending signals in the form of waves. Two waves are shown in the diagram with concentric circular wave fonts. The crest and trough are marked as bold and dashed circles respectively. The points where the bold circles of the two different waves meet are marked as points of constructive interference. Arrows point outward from the antenna, joining these points. These arrows show the directions of constructive interference.
An overhead view of two radio broadcast antennas sending the same signal, and the interference pattern they produce.

Can an antenna be any length? Explain your answer.

Problems&Exercises

What is the maximum electric field strength in an electromagnetic wave that has a maximum magnetic field strength of 5 . 00 × 10 − 4 T size 12{5 "." "00"´"10" rSup { size 8{-4} } " T"} {} (about 10 times the Earth’s)?

150 kV/m

The maximum magnetic field strength of an electromagnetic field is 5 × 10 − 6 T size 12{5 times "10" rSup { size 8{ - 6} } T} {} . Calculate the maximum electric field strength if the wave is traveling in a medium in which the speed of the wave is 0.75 c size 12{c} {} .

Verify the units obtained for magnetic field strength B in [link] (using the equation B = E c ) are in fact teslas (T).
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Source:  OpenStax, General physics ii phy2202ca. OpenStax CNX. Jul 05, 2013 Download for free at http://legacy.cnx.org/content/col11538/1.2
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