Electromagnetic Waves Questions

[whitehorsey]

1. In an EM wave traveling west, the B field oscillates vertically and has a frequency of 88.8 kHz and an rms strength of 7.8 * 10^-9 T. Determine the frequency and rms strength of the electric field. What is its direction?

The electric field of an electromagnetic wave is given by E_x=E₀ cos(kz + ωt), E_y = E_z = 0. Determine (a) the direction of propagation and (b) the magnitude and direction of B.2. E_max = B_max*c3. For the first problem, I know how to find rms by using the equation above. What I don't understand is why the frequencies for the electric field and magnetic field are equal and why the direction of the electric field is north-south.

The second question I'm also stuck on how to find the direction. Would it be similar to a traveling wave where if x and vt have the same sign then the wave travels in the decreasing x direction? So in this case it is in the decreasing z direction?

 

[tiny-tim]

hi whitehorsey!

What I don't understand is why the frequencies for the electric field and magnetic field are equal and why the direction of the electric field is north-south.

essentially, because they're the same field! (the electromagnetic field)

so you'd obviously expect them to have the same frequency, and slightly less obviously you'd expect them to have the same amplitude (subject to a "scaling" factor, c, which would just be 1 if we used more sensible units! )

the E and B fields are parts of the same field because they're interchangeable

(a bit like different components of the same force)​

if you change the velocity of the observer, the E and B forces interchange slightly

(a bit like F_xcosθ + F_ysinθ)​

but E² - (cB)² is constant (an invariant), and so is E.B

for a wave, those constants are both 0, ie for any observer, the amplitudes are the same and the fields are perpendicular

The second question I'm also stuck on how to find the direction. Would it be similar to a traveling wave where if x and vt have the same sign then the wave travels in the decreasing x direction? So in this case it is in the decreasing z direction?

yes …

to find the direction, change t by a certain amount (choose something convenient like 2π/ω), and ask yourself what else do i have to change to leave the equation the same?

obviously, decrease z ! ​

 

[whitehorsey]

Thanks! ^_^

-z is the direction the wave propagates. How would I be able to tell the direction for the electromagnetic wave?
In this example, E = $\widehat{}i$ E₀ cos(kz + ωt) would it be positive x - direction because there is no negative in front like this E = - $\widehat{}i$ E₀ cos(kz + ωt) [ This one would be negative x - direction?] ? Or is there a rule?

 

[rude man]

Thanks! ^_^

-z is the direction the wave propagates. How would I be able to tell the direction for the electromagnetic wave?
In this example, E = $\widehat{}i$ E₀ cos(kz + ωt) would it be positive x - direction because there is no negative in front like this E = - $\widehat{}i$ E₀ cos(kz + ωt) [ This one would be negative x - direction?] ? Or is there a rule?

If the E or B wave is given as cos(kz - wt) the wave travels in the +z direction. If the wave is given as cos(kz + wt) the wave travels in the -z direction. Has nothing to do with the sign or direction of E or B.

How do we know? Let z = 0 when t = 0 so you're at the peak of the wave. Then, some short time t later, the wave cos(kz - wt) peaks when cos(kz - wt) = 1 or kz - wt = 0 or z = wt/k so the peak has gone in the positive z direction.

If the wave is cos(kz + wt) then at time t the peak is when kz + wt = 0 or z = - wt/k so z is negative & the peak is going in the -z direction.

Same is true for waves of sin(kz - wt) vs. sin(kz + wt) or indeed any function f(kz - wt) vs. f(kz + wt).

 

[whitehorsey]

Thank You!