Answer to Question #88565 in Electricity and Magnetism for Priyanshu

Question #88565
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=B0μ0ɛ0=103×3×108=3×105(1)E_0=\frac {B_0} {\sqrt{\mu_0 ɛ_0} }= 10^{-3} \times3 \times10^8= 3 \times 10^5 (1)

β=ωc=2π×10×103c=π150(2)β=\frac {ω} {c}=\frac {2\pi\times10 \times10^3} {c}=\frac {\pi} {150} (2)

The incident wave fields:

Ei=3×105×cos(2π×104π150y)x^E_i=3 \times 10^5 \times {\cos (2\pi \times 10^4- \frac {\pi} {150} y)} \widehat{-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

r=k2k1k2+k1(3)r= \frac {k_2-k_1} { k_2+k_1} (3)k1=μ0ɛ0=120πk_1=\sqrt{\frac {\mu_0} { ɛ_0}}=120\pi

k2=μ2ɛ2=180πk_2=\sqrt{\frac {\mu_2} { ɛ_2}}=180\pi

We got: r=0.2



t=2k2k2+k1t=\frac {2k_2} {k_2+k_1}

We got: t =1.2


Reflected vector


Er=0.6×105×cos(2π×104tπ150y)x^E_r=0.6 \times 10^5 \times \cos{(2\pi \times 10^4 t - \frac {\pi} {150} y)} \widehat{x}

Transmitted vector


Et=3.6×105×cos(2π×104π150y)x^E_t =3.6 \times 10^5 \times \cos{(2\pi \times 10^4 - \frac {\pi} {150} y)} \widehat{-x}

Answer:

The incident vector


Ei=3×105×cos(2π×104π150y)x^E_i=3 \times 10^5 \times {\cos (2\pi \times 10^4- \frac {\pi} {150} y)} \widehat{-x}

Reflected vector


Er=0.6×105×cos(2π×104tπ150y)x^E_r=0.6 \times 10^5 \times \cos{(2\pi \times 10^4 t - \frac {\pi} {150} y)} \widehat{x}

Transmitted vector


Et=3.6×105×cos(2π×104π150y)x^E_t =3.6 \times 10^5 \times \cos{(2\pi \times 10^4 - \frac {\pi} {150} y)} \widehat{-x}


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Comments

Assignment Expert
29.04.19, 16:45

Dear Priyanshu, You're welcome. We are glad to be helpful. If you liked our service please press like-button beside answer field. Thank you!

Priyanshu
27.04.19, 18:34

Thank you very much Sir/Mam

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