So im having problems solving this problem. I don't see what im doing wrong. Here is the question.
An electromagnetic wave with frequency 65.0Hz travels in an insulating magnetic material that has dielectric constant 3.64 and relative permeability 5.18 at this frequency. The electric field has amplitude 7.20×10−3V/m.
A) What is the speed of propagation of the wave.
At first im like "OH speed of light 3*10^8" cuz its a wave. WRONG
So I look it up online. At this link it shows the speed formula for a propagating wave.
en.wikipedia.org/wiki/Wave_propagation_speed
Here i see VF (propagation speed) = 1/ sqrt(k) k being dielectric constant. Ans: 0.439 WRONG
So im stuck on that problem pretty good.
B)What is the wavelength of the wave.
"Oh this is an easy one. wavelength = c/f"
so w = 3*10^8 / 65.0 Hz = 4615384 WRONG
C)How would I go about finding the amplitude of magnetic field?
D) Also how would you find the intensity?
Thanks for any help. If you don't know how to do them all, just explain how to do the one's you know how to.
Answers (1)
A) Speed = 1/√(με) = 1/√(5.18*μ₀3.64ε₀) = {1/√(5.18*3.64 )}{1/√(μ₀ε₀)} = {c/√(5.18*3.64 )}, because
c = {1/√(μ₀*ε₀)} = 3*10⁸ m/s
So the required speed in the medium = [{3*(10⁸)}/{√(5.18*3.64 )}] = 6.91*10⁷ m/s
[Important point is that velocity is the property of the medium. Frequency is the property of the source and wavelength in different media is different because velocity is different and frequency times wavelength = velocity.]
B) With explanation above, the required wavelength λ in the medium = [{6.91*(10⁷)}/65] = 1.063*10⁶ m or 1063 km
C){√(5.18*μ₀)}B=√(3.64ε₀)}E or B = [{√(3.64*8.85*10⁻¹²}/{√(5.18*4π*10⁻⁷)}]*7.20*10⁻³ = 1.60*10⁻⁵ T
D) Intensity = [1/{5.18*4*π10⁻⁷}]|E||B| = [{7.20(10⁻³)1.60*10⁻⁵}/{4*5.18π*10⁻⁷}] = 1.77*10⁻² W/m²