Final answer:
The electric field strength at a distance of 100 feet from a cordless phone emitting 4.0 mW at 5.8 GHz can be calculated by first determining the intensity at that range and then using the relationship between intensity and electric field strength in free space.
Step-by-step explanation:
To calculate the electric field strength at a distance from a source emitting electromagnetic waves, we can use the formula for the intensity of the wave and then relate this to the electric field. The intensity I at a distance r from a point source of power P is given by I = P / (4πr2), assuming that the power spreads out uniformly in all directions as a sphere. To find the electric field strength E, we use the relationship I = (ε0 c E2) / 2, where ε0 is the permittivity of free space and c is the speed of light.
Now, given that the power P is 4.0 mW or 0.004 W and the range is 100 feet, first, convert the distance to meters (1 foot = 0.3048 meters): the result is approximately 30.48 meters. We can then calculate I, and with the value of I, solve for E using the second formula mentioned above.
Let's start by finding I at the 30.48-meter range:
- Calculate the area of a sphere with a radius of 30.48 m: A = 4πr2
- Determine the intensity at this range: I = P / A
- Use the relationship between intensity and electric field strength to solve for E.
Now we have all the steps needed to calculate the electric field strength at a distance of 100 feet from the phone.