Electromagnetic Waves (concept)

[calvert11]

Homework Statement

Given the electromagnetic wave traveling in the y direction at velocity c:

B = +cEo sin(k y − ω t) ˆi.

a) What happens to the ratio of the electric to magnetic field if the angular velocity ω of the
wave is decreased? Does it decrease, increase, or remain the same?

b) What happens to the velocity of the wave if the angular velocity ω of the wave is decreased? Does the velocity decrease, increase, or remain the same?

c) What happens to the the wavelength of the wave if the angular velocity ω of the wave is
decreased? Does the wavelength decrease, increase, or remain the same?

Homework Equations

E/B = v
v= ω/k
λ/c = 2*π/ω

The Attempt at a Solution

a) My guess: Since v= ω/k, decreasing ω would decrease v. So, if E/B = v, and v is decreasing, E/B also decreases. I think the ratio decreases. (INCORRECT)

b) My guess: Since v=ω/k, velocity decreases as ω decreases. I think the velocity decreases.

c) My guess: Wavelength is inversely related to angular velocity by λ/c = 2*π/ω. So, if angular velocity decreases, the wavelength increases. I think the wavelength increases.

 

[kuruman]

All electromagnetic waves in vacuum travel at the speed of light c regardless of their frequency or wavelength. Start from there and reconsider your answers.

 

[tomcue]

(INCORRECT)



a) Your reasoning is partially correct. As the angular velocity ω decreases, the velocity of the wave also decreases. However, the ratio of the electric to magnetic field actually increases. This is because the electric and magnetic fields are directly proportional to the velocity of the wave, and as the velocity decreases, the electric and magnetic fields decrease at a slower rate, resulting in an increase in their ratio.

b) As mentioned in part a, the velocity of the wave decreases as the angular velocity ω decreases. This is because the velocity of the wave is directly proportional to the angular velocity ω.

c) Your reasoning is again partially correct. As the angular velocity ω decreases, the wavelength actually decreases as well. This is because the wavelength is inversely proportional to the angular velocity, so as the angular velocity decreases, the wavelength decreases.