Question

a radio broadcast antenna is located at the top of a steep tall mountain. the antenna is broadcasting 104.3 fm (in megahertz) with a mean power of kilowatts. electfieldamplitude what is the intensity of the signal at a receiving antenna located away?

Answer 1

The intensity of the signal at a receiving antenna located 15 km away is 0.037 W/
`m^2`

Peak voltage generated in a straight wire antenna that is 0.9 m long (also located 15 km away) is 1.044 x
`10^(-12)` W / m

The peak voltage generated in a circular loop antenna which is 10 cm in radius (also located 15 km away) Vpeak = 0.73 x
`10^(-12)` W / m

The intensity of the signal at a distance of 15 km can be calculated using the following formula:

intensity = power / (4 x π x
`distance^2`)

where:

intensity is in watts per square meter (W/
`m^2`)

power is in watts (W)

distance is in meters (m)

Plugging in the known values, we get the following:

intensity = 7000 W / (4 × π × 15000
`m^2`)

intensity = 0.037 W/
`m^2`

The peak voltage generated in a straight wire antenna can be calculated using the following formula:

V peak = intensity x antenna length

where:

V peak is in volts (V)

antenna length is in meters (m)

Plugging in the known values, we get the following:

V peak = 1.16 x
`10^(-12)` W/
`m^2` x 0.9 m

V peak = 1.044 x
`10^(-12)` W / m

The peak voltage generated in a circular loop antenna can be calculated using the following formula:

V peak = intensity x antenna circumference

Now, we can plug this value into the formula for V peak:

V peak = intensity * antenna circumference

V peak = 1.16 x
`10^(-12)` W/
`m^2` x 0.63 m

V peak = 0.73 x
`10^(-12)` W / m