A simusoidal electromagnetic wave emitted by a cellular...

A simusoidal electromagnetic wave emitted by a cellular phone has a wavelength of 35.4 $\mathrm{cm}$ and an electric-field amplitude of $5.40 \times 10^{-2} \mathrm{V} / \mathrm{m}$ at a distance of 250 $\mathrm{m}$ from the antenna. Calculate (a) the frequency of the wave; (b) the magnetic-field amplitude; (c) the intensity of the wave.

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Key Concepts

Electromagnetic Waves

Electromagnetic waves are oscillations of electric and magnetic fields that propagate through space at the speed of light. They can travel through a vacuum as well as through various media, and their behavior is governed by Maxwell's equations.

Wave Frequency and Wavelength Relationship

The frequency of an electromagnetic wave is directly related to its wavelength through the speed of light, following the fundamental relation frequency = speed/wavelength. This inverse relationship is critical in determining one property when the other is known.

Interrelation of Electric and Magnetic Fields

In an electromagnetic wave, the electric and magnetic fields are perpendicular to each other and oscillate in phase. Their amplitudes are connected by the speed of light, meaning that knowing one field’s amplitude allows calculation of the other’s amplitude.

Intensity and Energy Transmission

The intensity of an electromagnetic wave, defined as the power transmitted per unit area, quantifies how much energy is carried by the wave. It is typically determined using the square of the amplitude of the electric field (or equivalently, through the Poynting vector), linking the measurable field strengths to the energy flux.

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