Question

Assume the local public radio station KUAF radiates 50000W of power in radio waves uniformly in all directions (in a uniform sphere). (a)What is the intensity of the waves at 1km = 1000m from the station? (b)What is the maximum amplitude of the electric field at 1km from the station? (c)What is the maximum amplitude of the magnetic field at 1km?

Answer 1

To solve this problem it is necessary to apply the equations related to intesity of plane electromagnetic wave, velocity of Speed, area of a Sphere and the permittivity of free space.

For definition we know that Intensity is equal to,

`I = (P)/(A)`

Where,

P = Power

A = Area (At this case sphere)

PART A) Using this definition the Intensity would be,

`I = (P)/(A)`

`I = (P)/(4\pi *r^2)`

`I = (5*10^4)/(4\pi *(10^3)^2)`

`I = 3.98*10^(-3) W/m^2`

PART B) To calculate the maximum amplitud of electric field we can use the definition the intesity of plane electromagnetic wave, that is

`I = (1)/(2) \epsilon_0 E_0^2 c`

Where,

`\epsilon_0 =`Constant of permittivity of free space

c = Speed of light

`E_0 =`Amplitude of the electric field

Replacing we have that,

`I = (1)/(2) \epsilon_0 E_0^2 c`

`3.98*10^(-3)= (1)/(2) (8.85*10^(-12)) E_0^2 3*10^8`

Re-arrange to find
`E_0,`

`E_0 = 1.731 V/m`

PART C) The amplitude of the magnetic field would be given by

`B_0 = (E_0)/(c)`

Where,

`E_0 =` Amplitude of the electric field

c = Speed of light

Replacing,

`B_0 = (1.731)/(3*10^8)`

`B_0 = 5.77*10^(-9)T`