# Electromagnetic waves waves review

1. Jun 10, 2012

### Color_of_Cyan

1. The problem statement, all variables and given/known data
The figure below shows a plane electromagnetic sinusoidal wave propagating in the x direction. Suppose the wavelength is 56.0 m and the electric field vibrates in the xy plane with an amplitude of 20.0 V/m.

(a) Calculate the frequency of the wave.

(b) Calculate the magnetic field when the electric field has its maximum value in the negative y direction.

(c) Write an expression for with the correct unit vector, with numerical values for Bmax, k, and ω, and with its magnitude in the form
B = Bmax cos (kx − ωt).
(Assume B is measured in nT, x is measured in m and t in s.)

2. Relevant equations

c = 1/(μ0ε0)1/2

c = 299609581 m/s

f = c / λ

E = Emax cos(kx - ωt)

B = Bmax cos(kx - ωt)

E max / B max = E / B = c

k = 2π/λ

ω = 2πf

3. The attempt at a solution

I only found the frequency, which is 5.35 x 106 Hz

I would like some hints how to find E max then I can just use the third equation listed.

I'm thinking that E = Emax cos(kx - wt) and I think

E = (20V/m) cos[(0.1121)(x) - (33615041)(t)]

where 0.1121 is k (k=2pi / λ)

and where 33615041 is ω (ω = 2πf)

What would I do with regards to x and t in the equation?

2. Jun 10, 2012

### Muphrid

The amplitude of the wave is given to you, and that is the magnitude of the electric field when it is maximal, isn't it?

Edit: wait, why are you asking about $E_\text{max}$ when you already observed it's $20 \; \text{V/m}$

3. Jun 10, 2012

### Color_of_Cyan

I didn't really see that... thanks

I got the rest of the problem as well.

Last edited: Jun 10, 2012