A radio antenna broadcasts a 1.0 MHz radio wave with 25 kW...

A radio antenna broadcasts a 1.0 MHz radio wave with $25 \mathrm{kW}$ of power. Assume that the radiation is emitted uniformly in all directions.
a. What is the wave's intensity $30 \mathrm{km}$ from the antenna?
b. What is the electric field amplitude at this distance?

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Key Concepts

Electromagnetic Wave Propagation

Electromagnetic waves, such as radio waves, propagate through space by spreading out as spherical wavefronts when emitted isotropically. This geometrical spreading is key to understanding how the energy is distributed in space and how measurements such as intensity decrease with increasing distance from the source.

Electric Field Amplitude Relation

The electric field amplitude of an electromagnetic wave is directly related to the wave’s intensity. In free space, the intensity and the electric field amplitude are connected by the relation I = 0.5??cE², where I is the intensity, ?? is the vacuum permittivity, c is the speed of light, and E is the electric field amplitude. This relationship bridges the macroscopic observable (intensity) with the microscopic oscillations of the electromagnetic field.

Intensity and Inverse Square Law

Intensity in the context of wave propagation is defined as the power per unit area. For a source radiating uniformly in all directions, power spreads out over the surface of a sphere, and the intensity at a given distance is determined by dividing the total power by the surface area of a sphere (4?r²). This relationship, often referred to as the inverse square law, shows that intensity diminishes as the square of the distance from the source increases.

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