# Consider a cell phone that emits electromagnetic radiation with a frequency of 1.0 GHz and with a...

## Question:

Consider a cell phone that emits electromagnetic radiation with a frequency of 1.0 GHz and with a power of 70 W.

(a) What is the electric field amplitude at a distance 1110 m away from the phone? Assume it radiates as a point source.

(b) If your ear is only about 10 cm from the source of radiation, what is the electric field amplitude at your ear as you use the phone? Again assume the phone radiates as a point source.

(c) If the phone can be turned on and stays transmitting for 2 h before discharging the battery, how much energy can be stored in the battery?

## Electric Fields in EM waves:

Electromagnetic waves are made up of oscillating magnetic and electric fields. The intensity of the wave, which in formal definition is the power emitted over the area where it is applied, can also be expressed in terms of the electric field amplitude as:

{eq}\displaystyle I = \frac{c\epsilon_0 E^2}{2} {/eq}

where:

- {eq}\displaystyle c = 3\ \times\ 10^8\ m/s {/eq} is the speed of light

- {eq}\displaystyle \epsilon_0 = 8.85\ \times\ 10^{-12}\ F/m {/eq} is the permittivity in free space constant

*E*is the electric field amplitude

## Answer and Explanation: 1

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Given:

- {eq}\displaystyle P = 70\ W {/eq} is the power emitted

- {eq}\displaystyle f = 1\ GHz = 1\ \times\ 10^9\ Hz {/eq} is the EM wave frequency

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Chapter 20 / Lesson 6Electromagnetic waves are both electric and magnetic, and can travel without a medium. Learn about the definition, sources, and properties of electromagnetic waves.