Electric and Magnetic Waves: Moving Together

Following Ampere’s law, current in the antenna produces a magnetic field, as shown in Figure 2. The relationship between $latex \boldsymbol{E} $ and $latex \boldsymbol{B} $ is shown at one instant in Figure 2 (a). As the current varies, the magnetic field varies in magnitude and direction.

The magnetic field lines also propagate away from the antenna at the speed of light, forming the other part of the electromagnetic wave, as seen in Figure 2 (b). The magnetic part of the wave has the same period and wavelength as the electric part, since they are both produced by the same movement and separation of charges in the antenna.

The electric and magnetic waves are shown together at one instant in time in Figure 3. The electric and magnetic fields produced by a long straight wire antenna are exactly in phase. Note that they are perpendicular to one another and to the direction of propagation, making this a transverse wave.

Electromagnetic waves generally propagate out from a source in all directions, sometimes forming a complex radiation pattern. A linear antenna like this one will not radiate parallel to its length, for example. The wave is shown in one direction from the antenna in Figure 3 to illustrate its basic characteristics.

Instead of the AC generator, the antenna can also be driven by an AC circuit. In fact, charges radiate whenever they are accelerated. But while a current in a circuit needs a complete path, an antenna has a varying charge distribution forming a standing wave, driven by the AC. The dimensions of the antenna are critical for determining the frequency of the radiated electromagnetic waves. This is a resonant phenomenon and when we tune radios or TV, we vary electrical properties to achieve appropriate resonant conditions in the antenna.

Receiving Electromagnetic Waves

Electromagnetic waves carry energy away from their source, similar to a sound wave carrying energy away from a standing wave on a guitar string. An antenna for receiving EM signals works in reverse. And like antennas that produce EM waves, receiver antennas are specially designed to resonate at particular frequencies.

An incoming electromagnetic wave accelerates electrons in the antenna, setting up a standing wave. If the radio or TV is switched on, electrical components pick up and amplify the signal formed by the accelerating electrons. The signal is then converted to audio and/or video format. Sometimes big receiver dishes are used to focus the signal onto an antenna.

In fact, charges radiate whenever they are accelerated. When designing circuits, we often assume that energy does not quickly escape AC circuits, and mostly this is true. A broadcast antenna is specially designed to enhance the rate of electromagnetic radiation, and shielding is necessary to keep the radiation close to zero. Some familiar phenomena are based on the production of electromagnetic waves by varying currents. Your microwave oven, for example, sends electromagnetic waves, called microwaves, from a concealed antenna that has an oscillating current imposed on it.

Relating E-Field and B-Field Strengths

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

Since current is directly proportional to voltage (Ohm’s law) and voltage is directly proportional to $latex \boldsymbol{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,

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

Example 1: Calculating B -Field Strength in an Electromagnetic Wave

What is the maximum strength of the $latex \boldsymbol{B} $ -field in an electromagnetic wave that has a maximum $latex \boldsymbol{E} $ -field strength of $latex \boldsymbol{1000 \;\textbf{V/m}} $?

Strategy

To find the $latex \boldsymbol{B} $ -field strength, we rearrange the above equation to solve for $latex \boldsymbol{B} $, yielding

Solution

We are given $latex \boldsymbol{E} $, and $latex \boldsymbol{c} $ is the speed of light. Entering these into the expression for $latex \boldsymbol{B} $ yields

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

Discussion

The $latex \boldsymbol{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 Chapter 24.1 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.

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.