The magnetic vector of a plane electromagnetic wave is described as follows:

B⃗ =Bmxˆsin[13 rad/m z− 3.90e9 rad/sec t] where Bm>0. This represents the full magnetic field, so that By=Bz=0.
(a) What is the wavelength λ of the wave, in meters?

(b) What is the frequency f of the wave, in cycles per second?

unanswered
(c) In which direction does this wave propagate?

(d) The associated electric field E⃗ (x⃗ ,t) can be written as

E⃗ =A0sin(kxx+kyy+kzz−ωt)mˆ
Where kx,ky,kz and ω are all positive.

Determine:
m

A0 in V/m, assuming Bm=9.43e-7 T. Note that A0 could be positive or negative.

kx in rad/m

ky in rad/m

kz in rad/m

ω in rad/s

(e) What is the time-averaged Poynting flux associated with this wave, assuming Bm=9.43e-7 T?
direction:

magnitude in W/m2:

anyone????

To find the answers to these questions, we will use the given information:

B⃗ = Bmxˆsin[13 rad/m z − 3.90e9 rad/sec t]

where Bm > 0, By = Bz = 0.

(a) To find the wavelength λ of the wave, we can use the equation:

λ = 2π/k

where k is the wave vector. From the given equation, we can see that k = 13 rad/m. Plugging this into the equation gives:

λ = 2π/(13 rad/m)

Simplifying this expression will give you the value of λ in meters.

(b) To find the frequency f of the wave, we can use the equation:

f = ω/(2π)

where ω is the angular frequency. From the given equation, we can see that ω = 3.90e9 rad/sec. Plugging this into the equation gives:

f = (3.90e9 rad/sec)/(2π)

Simplifying this expression will give you the value of f in cycles per second.

(c) To determine the direction in which the wave propagates, we need to look at the wave equation:

B⃗ = Bmxˆsin[13 rad/m z − 3.90e9 rad/sec t]

The wave equation tells us that the wave is propagating in the z-direction, as the z-term is present. Therefore, the direction of propagation for this wave is along the positive z-axis.

(d) Now let's determine the values of m, A0, kx, ky, kz, and ω using the given information.

From the equation for the magnetic field:

B⃗ = Bmxˆsin[13 rad/m z − 3.90e9 rad/sec t]

we can see that Bx = Bmx, By = Bz = 0.

The associated electric field is given by:

E⃗ = A0sin(kxx + kyy + kzz − ωt)m^

Comparing this equation to the given magnetic field equation, we can identify the values of m, A0, kx, ky, kz, and ω.

m = 1 (as the magnetic field equation doesn't involve any m terms)
A0 = Bm (from the magnitude of the magnetic field equation)
kx = ky = kz = 13 rad/m (from the wave vector term)
ω = 3.90e9 rad/sec (from the angular frequency term)

(e) To find the time-averaged Poynting flux associated with this wave, we can use the equation:

Poynting Flux = (1/2) * (c/μ0) * E₀²

where E₀ is the electric field amplitude, c is the speed of light, and μ₀ is the vacuum permeability.

From the given information, we know that Bm = 9.43e-7 T. Since Bm is the amplitude of the magnetic field, we can use it as E₀ in the Poynting Flux equation.

Plugging in the values, we have:

Poynting Flux = (1/2) * (3.00e8 m/s)/(4π * 1.26e-6 T*m/A) * (9.43e-7 T)²

Simplifying this expression will give you the magnitude of the time-averaged Poynting flux in W/m².

To determine the direction of the Poynting flux, we can use the right-hand rule. Point your thumb in the direction of the electric field and curl your fingers. The direction your fingers point represents the direction of the Poynting flux.