Question

An electromagnetic wave in a vacuum traveling in the +x direction generated by a variable source initially has a

wavelength ? of 225 ?mand a maximum electric field Emax in the +ydirection of 7.40�10^-3 V/m .

If the period of the wave is then increased by a factor of 1.50, what is the equation of the

resulting magnetic field component of the wave?



What are the coefficients in the equation for the magnetic field component
of the wave after the period increases by a factor of 1.50?
Enter the maximum magnetic field, wavenumber,
and angular frequency in teslas, inverse meters, and radians per second separated by commas.

Answer 1

B (z) = 2,467 10⁻¹¹ cos (1,486 10⁸ x - 5.571 10¹⁵ t )

Step-by-step explanation:

An electromagnetic wave is a wave that is sustained in the perpendicular fluctuations of the electric and magnetic fields, the equation of the wave is

E (y) = Eo cos (kx –wt)

B (z) = Bo cos (kx-wt)

Let's look for the terms to build these equations. The speed of the wave is given by

c = λ f

The frequency and period are related

f = 1 / T

Let's start by applying this equation our case

f = c /λ

f = 3 10⁸/225 10⁻⁹

f = 1.33 10¹⁵ Hz

The angular velocity and the wave number are

w = 2π f

k = 2π /λ

w = 2π 1.33 10¹⁵ = 8.38 10¹⁵ rad / s

k = 2π / 225 10⁻⁹ = 2.79 10⁷ m⁻¹

It indicates that the period increases by a factor of 1.5, let's look for the new frequency

T = 1.5 T₀

f = 1 / T

f = 1 / 1.5T₀

f = 1 / 1.5 f₀

f = 1 / 1.5 1.33 10¹⁵ = 8.87 10¹⁴ Hz

c = λ f

λ = c / f

λ = 3 10⁸ / 8.87 10¹⁴ = 4,229 10⁻⁸ m

Let's find the new w and k

w = 2π f

w = 2π 8.87 10¹⁴ = 5.571 10¹⁵ rad/s

k = 2π / λ

k = 2π / 4,229 10⁻⁸ = 1,486 10⁸ cm⁻¹

We use the relationship that the fields are in phase

c = E₀ / B₀

B₀ = E₀ / c

B₀ = 7.4 10⁻³ / 3 10 ⁸ = 2.467 10⁻¹¹ T

With these values ​​we can build the equation of the magnetic field

B (z) = 2,467 10⁻¹¹ cos (1,486 10⁸ x - 5.571 10¹⁵ t )