A uniform plane wave of 10 kHz travelling in free space strikes a large block of a material having ε=9ε_0,μ=4μ_0 and σ=0 normal to the surface.If the incident magnetic field vector is given by B→=10^(-3) sin(ωt-βy)k^ tesla
Write the complete expression for the incident,reflected and transmitted field vectors.
Please explain in detail.
1
Expert's answer
2019-04-26T11:28:37-0400
The incident wave Ei has the magnitude
E0=μ0ɛ0B0=10−3×3×108=3×105(1)
β=cω=c2π×10×103=150π(2)
The incident wave fields:
Ei=3×105×cos(2π×104−150πy)−x
We assume that the incident electric field is reflected with a reflection coefficient Γ and transmitted with a transmitted with a transmission coefficient τ. That implies that if the electric field intensity of the incident, reflected and transmitted waves at the boundary (z = 0) are Ei0, Er0 and Et0 respectively, then Er0= rEi0 and Et0= t Ei0
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