∵Radio Reception A 125-kW radio station broadcasts its...

$\because$ Radio Reception $A 125-\mathrm{kW}$ radio station broadcasts its signal uniformly in all directions. (a) What is the average intensity of its signal at a distance of 8.05 $\mathrm{km}$ from the station? (b) What is the rms value of the electric field in this radio wave? (c) If a $1.22-\mathrm{m}$ receiving antenna is oriented parallel to the electric field of the radio wave, what rms voltage appears between its ends?

$\because$ Radio Reception $A 125-\mathrm{kW}$ radio station broadcasts its signal
uniformly in all directions. (a) What is the average intensity of its
signal at a distance of 8.05 $\mathrm{km}$ from the station? (b) What is the
rms value of the electric field in this radio wave? (c) If a $1.22-\mathrm{m}$
receiving antenna is oriented parallel to the electric field of the
radio wave, what rms voltage appears between its ends?

Key Concepts

Relationship between Electric Field and Intensity in Electromagnetic Waves

In electromagnetic wave theory, the intensity is related to the electric field amplitude by the equation I = 1/2 c ?? E² (for rms values in the context of sinusoidal waves). This relation provides a means to calculate the magnitude of the electric field based on the known intensity, linking the energy carried by the wave to the field strengths.

Antenna Voltage Induction

When a receiving antenna is aligned with the electric field of an electromagnetic wave, the induced voltage across it is directly proportional to the product of the electric field strength and the effective length of the antenna. This concept is essential for understanding how electromagnetic waves can be detected and converted into electrical signals by practical antennas.

Inverse Square Law

This principle explains that the intensity of radiation from a point source decreases as the square of the distance from the source increases, because the energy is spread uniformly over the surface of a sphere whose area grows as 4?r². It’s fundamental for calculating the power per unit area at a specified distance from a radiating source.

Intensity of Spherical Waves

For a source emitting energy uniformly in all directions, the intensity (or power density) at any distance is determined by dividing the total power by the surface area of a sphere with that radius. This concept is crucial for connecting the source’s power output with the measurable energy arriving at a distance.

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