Question

WGVU-AM is a radio station that serves the Grand Rapids, Michigan area. The main broadcast frequency is 1480kHz. At a certain distance from the radio station transmitter, the magnitude of the magnetic field of the electromagnetic wave is 3.0x10^-11T.

a. Calculate the wavelength
b. What is the angular velocity?
c. Find the wave number of the wave.
d. What is the amplitude of the electric field at this distance from the transmitter?

Answer 1

a

`\lambda = 202.7 \ m`

b

`w = 9.3 *10^(6) \ rad/s`

c

`k = 0.031 m^(-1)`

d

`E_(max) = 9.0 *10^(-3) \ V/m`

Step-by-step explanation:

From the question we are told that

The frequency of the radio station is
`f= 1480 \ kHz = 1480 *10^(3)\ Hz`

The magnitude of the magnetic field is
`B = 3.0* 10^(-11) \ T`

Generally the wavelength is mathematically represented as

`\lambda = (c)/(f)`

Here c is the speed of light with value
`c = 3.0 *10^(8) \ m/s`

So

`\lambda = (3.0 *10^(8))/( 1480 *10^(3))`

=>
`\lambda = 202.7 \ m`

Generally the angular frequency is mathematically represented as

`w = 2 \pi * f`

=>
`w = 2 * 3.142 * 1480 *10^(3)`

=>
`w = 9.3 *10^(6) \ rad/s`

Generally the wave number is mathematically represented as

=>
`k = (2 \pi )/(\lambda)`

=>
`k = (2 * 3.142 )/( 202.7)`

=>
`k = 0.031 m^(-1)`

Generally the amplitude of the electric field at this distance from the transmitter is mathematically represented as

`E_(max) = c * B`

=>
`E_(max) = 3.0 *10^(8) * 3.0* 10^(-11)`

=>
`E_(max) = 9.0 *10^(-3) \ V/m`