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# EM Fields Help

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## Introduction

Isaac Newton believed that visible light is composed of tiny particles, or corpuscles . Today we recognize these particles as photons. However, light is more complex than can be represented by the particle theory. It has wave-like characteristics too. The same is true of all forms of radiant energy.

## EM Fields

The wave nature of radiant energy is the result of interaction of electricity and magnetism. Charged particles, such as electrons and protons, are surrounded by electrical fields . Magnetic poles or moving charged particles produce magnetic fields . When the fields are strong enough, they extend a considerable distance. When electrical and magnetic fields vary in intensity, we have an electromagnetic (EM) field .

## Static Fields

You have observed the attraction between opposite poles of magnets and the repulsion between like poles. Similar effects occur with electrically charged objects. These forces seem to operate only over short distances under laboratory conditions, but this is so because such fields weaken rapidly, as the distance between poles increases to less than the smallest intensity we can detect. In theory, the fields extend into space indefinitely.

A constant electric current in a wire produces a magnetic field around the wire. The lines of magnetic flux are perpendicular to the direction of the current. The existence of a constant voltage difference between two nearby objects produces an electrical field; the lines of electrical flux are parallel to the gradient of the charge differential. When the intensity of a current or voltage changes with time, things get more interesting.

## Fluctuating Fields

A fluctuating current in a wire or a variable charge gradient between two nearby objects gives rise to a magnetic field and an electrical field in combination. These fields leapfrog through space so that the EM field can travel long distances with less attenuation than either an electrical field or a magnetic field alone. The electrical and magnetic fields in such a situation are perpendicular to each other everywhere in space. The direction of travel of the resulting EM field is perpendicular to both the electrical and magnetic lines of flux, as shown in Fig. 18-1.

Fig. 18-1 . An EM wave is comprised of fluctuating, mutually perpendicular electrical and magnetic lines of flux. The field travels perpendicular to both sets of flux lines.

In order for an EM field to exist, the electrons in a wire or other conductor not only must be set in motion, but they also must be accelerated. That is, their velocity must be made to change. The most common method of creating this sort of situation is the introduction of an alternating current (ac) in an electrical conductor. It also can result from the bending of charged-particle beams by electrical or magnetic fields.

## Frequency And Wavelength

EM waves travel through space at the speed of light, which is approximately 2.99792 × 10 8 m/s (1.86262 × 10 5 mi/s). This is often rounded up to 3.00 × 10 8 m/s, expressed to three significant figures. The wavelength of an EM field in free space gets shorter as the frequency becomes higher. At 1 kHz, the wavelength is about 300 km. At 1 MHz, the wavelength is about 300 m. At 1 GHz, the wavelength is about 300 mm. At 1 THz, an EM signal has a wavelength of 0.3 mm—so small that you would need a magnifying glass to see it.

The frequency of an EM wave can get much higher than 1 THz; some of the most energetic known rays have wavelengths of 0.00001 Ångström (10 −5 Å). The Ångström is equivalent to 10 −10 m and is used by some scientists to denote extremely short EM wavelengths. A microscope of great magnifying power would be needed to see an object with a length of 1 Å. Another unit, increasingly preferred by scientists these days, is the nanometer (nm), where 1 nm = 10 −9 m = 10 Å.

The formula for wavelength λ, in meters, as a function of the frequency f , in hertz, for an EM field in free space is

λ = 2.99792 × 10 8 / f

This same formula can be used for λ in millimeters and f in kilohertz, for λ in micrometers and f in megahertz, and for λ in nanometers and f in gigahertz. Remember your prefix multipliers: 1 millimeter (1 mm) is 10 −3 m, 1 micrometer (1 μm) is 10 −6 m, and 1 nanometer (1 nm) is 10 −9 m.

The formula for frequency f , in hertz, as a function of the wavelength λ, in meters, for an EM field in free space is given by transposing f and λ in the preceding formula:

f = 2.99792 × 10 8

As in the preceding case, this formula will work for f in kilohertz and λ in millimeters, for f in megahertz and λ in micrometers, and for f in gigahertz and λ in nanometers.

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