# 24.2 Production of electromagnetic waves

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## Learning objectives

By the end of this section, you will be able to:

• Describe the electric and magnetic waves as they move out from a source, such as an AC generator.
• Explain the mathematical relationship between the magnetic field strength and the electrical field strength.
• Calculate the maximum strength of the magnetic field in an electromagnetic wave, given the maximum electric field strength.

The information presented in this section supports the following AP® learning objectives and science practices:

• 6.A.1.1 The student is able to use a visual representation to construct an explanation of the distinction between transverse and longitudinal waves by focusing on the vibration that generates the wave. (S.P. 6.2)
• 6.A.1.2 The student is able to describe representations of transverse and longitudinal waves. (S.P. 1.2)
• 6.A.2.2 The student is able to contrast mechanical and electromagnetic waves in terms of the need for a medium in wave propagation. (S.P. 6.4, 7.2)
• 6.B.3.1 The student is able to construct an equation relating the wavelength and amplitude of a wave from a graphical representation of the electric or magnetic field value as a function of position at a given time instant and vice versa, or construct an equation relating the frequency or period and amplitude of a wave from a graphical representation of the electric or magnetic field value at a given position as a function of time and vice versa. (S.P. 1.4)
• 6.F.2.1 The student is able to describe representations and models of electromagnetic waves that explain the transmission of energy when no medium is present. (S.P. 1.1)

We can get a good understanding of electromagnetic waves    (EM) by considering how they are produced. Whenever a current varies, associated electric and magnetic fields vary, moving out from the source like waves. Perhaps the easiest situation to visualize is a varying current in a long straight wire, produced by an AC generator at its center, as illustrated in [link] .

The electric field    ( $\mathbf{E}$ ) shown surrounding the wire is produced by the charge distribution on the wire. Both the $\mathbf{E}$ and the charge distribution vary as the current changes. The changing field propagates outward at the speed of light.

There is an associated magnetic field    ( $\mathbf{B}$ ) which propagates outward as well (see [link] ). The electric and magnetic fields are closely related and propagate as an electromagnetic wave. This is what happens in broadcast antennae such as those in radio and TV stations.

Closer examination of the one complete cycle shown in [link] reveals the periodic nature of the generator-driven charges oscillating up and down in the antenna and the electric field produced. At time $t=0$ , there is the maximum separation of charge, with negative charges at the top and positive charges at the bottom, producing the maximum magnitude of the electric field (or $E$ -field) in the upward direction. One-fourth of a cycle later, there is no charge separation and the field next to the antenna is zero, while the maximum $E$ -field has moved away at speed $c$ .

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