Question

A certain 60.0 Hz AC power line radiates an electromagnetic wave having a maximum electric field strength of 11.6 kV/m.

a. What is the wavelength of this very low frequency electromagnetic wave?
b. What type of electromagnetic radiation is this wave?
c. What is its maximum magnetic field strength?

Answer 1

a)
`\lambda=5* 10^6\ m`

b) The wavelength of the obtained is greater than 1mm so it lies in the range of radio waves.

c)
`B_m=3.867* 10^(-5)\ T`

Step-by-step explanation:

Given:

frequency of electromagnetic waves,
`f=60\ Hz`

maximum field strength of the electric field,
`E_m=11600\ V.m^(-1)`

Since the velocity of electromagnetic waves is,
`c=3* 10^8\ m.s^(-1)`

a)

We know the relation between the frequency and wavelength is given as:

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

`\lambda=(3* 10^(8))/(60)`

`\lambda=5* 10^6\ m`

b)

The wavelength of the obtained is greater than 1mm so it lies in the range of radio waves.

c)

The maximum magnetic field can be calculated as:

`B_m=(E_m)/(c)`

`B_m=(11600)/(3* 10^8)`

`B_m=3.867* 10^(-5)\ T`

Answer 2

Step-by-step explanation:

Given that,

Frequency of the power line, f = 6 Hz

Value of maximum electric field strength of 11.6 kV/m

(a) The wavelength of this very low frequency electromagnetic wave is given by using relation as :

`c=f\lambda`

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

`\lambda=(3* 10^8\ m/s)/(60\ Hz)`

`\lambda=5* 10^6\ m`

(b) As its can be seen that the wavelength of this wave is very high. It shows that it is a radio wave.

(c) The relation between the maximum magnetic field strength and maximum electric field strength is given by :

`B_0=(E_0)/(c)\\\\B_0=(11.6* 10^3)/(3* 10^8)\\\\B_0=3.86* 10^(-5)\ T`

So, the maximum magnetic field strength is
`3.86* 10^(-5)\ T`.