Answer:
a
[tex]\lambda = 202.7 \ m[/tex]
b
[tex]w = 9.3 *10^{6} \ rad/s[/tex]
c
[tex]k = 0.031 m^{-1}[/tex]
d
[tex]E_{max} = 9.0 *10^{-3} \ V/m[/tex]
Explanation:
From the question we are told that
The frequency of the radio station is [tex]f= 1480 \ kHz = 1480 *10^{3}\ Hz[/tex]
The magnitude of the magnetic field is [tex]B = 3.0* 10^{-11} \ T[/tex]
Generally the wavelength is mathematically represented as
[tex]\lambda = \frac{c}{f}[/tex]
Here c is the speed of light with value [tex]c = 3.0 *10^{8} \ m/s[/tex]
So
[tex]\lambda = \frac{3.0 *10^{8}}{ 1480 *10^{3}}[/tex]
=> [tex]\lambda = 202.7 \ m[/tex]
Generally the angular frequency is mathematically represented as
[tex]w = 2 \pi * f[/tex]
=> [tex]w = 2 * 3.142 * 1480 *10^{3}[/tex]
=> [tex]w = 9.3 *10^{6} \ rad/s[/tex]
Generally the wave number is mathematically represented as
=> [tex]k = \frac{2 \pi }{\lambda}[/tex]
=> [tex]k = \frac{2 * 3.142 }{ 202.7}[/tex]
=> [tex]k = 0.031 m^{-1}[/tex]
Generally the amplitude of the electric field at this distance from the transmitter is mathematically represented as
[tex]E_{max} = c * B[/tex]
=> [tex]E_{max} = 3.0 *10^{8} * 3.0* 10^{-11}[/tex]
=> [tex]E_{max} = 9.0 *10^{-3} \ V/m[/tex]
