Consider a cell phone that emits electromagnetic radiation...

Consider a cell phone that emits electromagnetic radiation with a frequency of $1.0 \mathrm{GHz}\left(1.0 \times 10^{9} \mathrm{Hz}\right)$ with a power of $1.0 \mathrm{W}$. a. What is the approximate electric field amplitude at a distance of $1000 \mathrm{m}$ from the phone? Assume it radiates with spherical wavefronts. b. What is the approximate electric field amplitude at your ear as you use the phone? Again assume it radiates with spherical wavefronts. c. If the phone can be turned on and transmitting for $3 \mathrm{h}$ before discharging the battery, how much energy can be stored in the battery?

Consider a cell phone that emits electromagnetic radiation with a frequency of $1.0 \mathrm{GHz}\left(1.0 \times 10^{9} \mathrm{Hz}\right)$ with a power of $1.0 \mathrm{W}$.
a. What is the approximate electric field amplitude at a distance of $1000 \mathrm{m}$ from the phone? Assume it radiates with spherical wavefronts.
b. What is the approximate electric field amplitude at your ear as you use the phone? Again assume it radiates with spherical wavefronts.
c. If the phone can be turned on and transmitting for $3 \mathrm{h}$ before discharging the battery, how much energy can be stored in the battery?

Key Concepts

Spherical Wavefronts and the Inverse Square Law

When electromagnetic waves are radiated uniformly in all directions from a point source, they form spherical wavefronts. As the wave propagates, its energy spreads over the surface of an expanding sphere, meaning the intensity of the wave drops off in proportion to 1/(distance)^2. This inverse square law is fundamental for predicting how field strengths decrease with distance.

Electromagnetic Wave Propagation

Electromagnetic waves are disturbances in the electric and magnetic fields that propagate through space carrying energy. These waves are characterized by properties such as frequency, amplitude, and polarization, and they obey the linear superposition principle. Their study explains how energy is transmitted away from a given source and how fields interact with matter.

Intensity and Electric Field Relationship

The intensity of an electromagnetic wave, which represents the power per unit area, is directly related to the square of the electric field amplitude, typically through the relation I = (1/2)??cE² for plane waves in free space. This relationship is key to determining the field amplitude given the known power and distance from the source.

Energy Consumption and Battery Storage

Energy consumption in electrical devices, like those using batteries, is determined by the product of power and operational time. This concept is essential for calculating the total energy a battery can store or deliver, independent of the nature of the electromagnetic phenomena involved.

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