Answer:
B(z,t) = 2,867 10⁻¹¹ cos (2.06 10⁴ x - 3,635 10¹² t)
Step-by-step explanation:
The wave equation for an electromagnetic wave is
E = E₀ cos (kx –wt)
B = B₀ cos (kx - wt)
Where these equations are for the electric and magnetic fields, respectively.
The two fields are related through the speed of light
c = E₀ / B₀
Let's apply to our case, the wavelength is 305 μm = 305 10⁻⁶ m, The wave number is
k = 2π / λ
k = 2π / 305 10⁻⁶
k = 2.06 10⁴ m
Period change to by a factor of 1.7, we write based on the initial period (T₀), the angular velocity is
w = 2π f
With the initial data and the relationship
c = λ f
f = c / λ
f = 3 10⁸/305 10⁻⁶6
.f = 9.836 10¹¹ Hz
The frequency and period are related
f = 1 / T
T = 1.7 T₀
f = 1 / 1.7 1 / T₀
f = 1 /1.7 9.836 10¹¹
f = 5,786 10¹¹ Hz
w = 2π f
w = 2π 5,786 10¹¹
w = 3,635 10¹² rad / s
We look for the maximum amplitude of the magnetic field
B₀ = E₀ / c
B₀ = 8.60 10⁻³ / 3 10⁸
B₀ = 2,867 10⁻¹¹ T
the fields and the velocity wave vector are perpendicular to each other, therefore the magnetic field oscillates in the z-direction
We build the equation of the magnetic field
B(z,t) = 2,867 10⁻¹¹ cos (2.06 10⁴ x - 3,635 10¹² t)