A radio station with a power of 20 kW sends out an omnidirectional wave at 1.25 MHz.
a. If the electromagnetic wave has an electric field of 0.22 V/m, what is the magnetic field amplitude?
b. What is the intensity of the wave at 5 km?
c. What is the wavelength of the electromagnetic wave?
after 50 years in radio, I have no idea what an omni-directional antenna is. Does it radiate upwards? Downward? in a Donut shape? It is easier to just say the gain in db in a particular direction, and stop the nonsense about omnidirectional antennas. This is a real world.
c) frequency*wovelength=speedofLight
solve for wavelength.
This is what is normally called omni-directional antenna patterns by radio users, it is not OMNI in the sense physicists mean, a spherical pattern. http://www.inl.gov/featurestories/i/antenna_02.jpg
In this pattern, one has to know the flatness in azimuth, which is complicated. It is just much easier to specify gain in db over a the mythical spherical omni, which does not exist.
That idea of "omni directional" kind of confused me also... I would guess that it can be assumed as just a regular wave?
To find the answers to the given questions, we can use the basic formulas that relate different parameters of electromagnetic waves. Here's how we can find each answer:
a. To find the magnetic field amplitude, we can use the relationship between the electric and magnetic fields in an electromagnetic wave, which is given by the formula:
E/B = c
where E is the electric field amplitude, B is the magnetic field amplitude, and c is the speed of light in a vacuum (approximately 3 x 10^8 m/s).
Rearranging the formula, we have:
B = E/c
Substituting the given values, we get:
B = 0.22 V/m / 3 x 10^8 m/s
Calculating this, we find the magnetic field amplitude.
b. To calculate the intensity of the wave at 5 km, we can use the inverse square law, which states that the intensity of a wave decreases as the square of the distance from the source. The formula for intensity (I) is given by:
I = P / (4πr^2)
where P is the power of the wave and r is the distance from the source.
Given that the power of the radio station is 20 kW, we need to convert it to watts by multiplying by 1000:
P = 20 kW * 1000 = 20,000 W
Substituting the other values, we have:
I = 20,000 W / (4π * (5,000 m)^2)
Evaluate this expression to find the intensity of the wave at 5 km.
c. The wavelength of an electromagnetic wave can be calculated using the formula:
λ = c / f
where λ is the wavelength, c is the speed of light, and f is the frequency of the wave.
Given that the frequency of the wave is 1.25 MHz, we need to convert it to Hz by multiplying by 10^6:
f = 1.25 MHz * 10^6 Hz/MHz = 1.25 x 10^6 Hz
Substituting the values into the formula, we have:
λ = 3 x 10^8 m/s / (1.25 x 10^6 Hz)
Evaluate this expression to find the wavelength of the electromagnetic wave.