## A plane monochromatic radio wave (? = 0.3 m) travels in vacuum along the positive x-axis, with a time-averaged intensity I = 45.0 W/m2. Supp

Question

A plane monochromatic radio wave (? = 0.3 m) travels in vacuum along the positive x-axis, with a time-averaged intensity I = 45.0 W/m2. Suppose at time t = 0, the electric field at the origin is measured to be directed along the positive y-axis with a magnitude equal to its maximum value. What is Bz, the magnetic field at the origin, at time t = 1.5 ns? Bz = I got .04800 but that answer didnt work.

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7 months 2021-07-15T19:57:58+00:00 1 Answers 50 views 0

The magnetic field

Explanation:

From the question we are told that

The wavelength is

The intensity is

The time is

Generally radiation intensity is mathematically represented as

Where  c is the speed of light with a constant value of

is the electric field

is the permittivity  of free space with a constant value of

Making the subject of the formula we have

Substituting values

Generally electric and magnetic field are related by the mathematical equation as follows

Where is the magnetic field

making   the subject

Substituting values

Next is to obtain the wave number

Generally  the wave number is mathematically represented as

Substituting values

Next is to obtain the frequency

Generally  the  frequency f is mathematically represented as

Substituting values

Next is to obtain the angular velocity

Generally  the  angular velocity   is mathematically represented as

Generally  the sinusoidal electromagnetic waves for the magnetic field B moving in the positive z direction is expressed as

Since the magnetic field is induced at the origin then the equation above is reduced to

x =0 because it is the origin we are considering

Substituting values