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Physics Question on Electromagnetic waves

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by E⃗=30(2x^+y^)sin[2π(5×1014−1073z)]Vm−1\vec{E}=30(2\hat{x}+\hat{y})sin[2\pi(5\times10^{14}-\frac{10^7}{3}z)]Vm^{-1}.
which of the following is correct? [given: speed of light in vacuum c=3×108c=3\times10^8 m/s]

A

The wave is E polarized in the x-y plane with a polarization angle 30° with respect to the x-axis.

B

The refractive index of medium is 2

C

By=2×10−7 sin[2π(5×1014t−1073z)]w8/m2B_y=2\times10^{-7}\,sin[2\pi(5\times10^{14}t-\frac{10^7}{3}z)]w^8/m^2

D

By=−2×10−7 sin[2π(5×1014t−1073z)]w8/m2B_y=-2\times10^{-7}\,sin[2\pi(5\times10^{14}t-\frac{10^7}{3}z)]w^8/m^2

Answer

The refractive index of medium is 2

Explanation

Solution

The correct answers are: (B)and(D).
(1) wave is polarized in X-Y plane, polarization angle is tan−1(12)tan^{-1}(\frac{1}{2})
(2) Refractive index of the medium = Cv\frac{C}{v}
when V=wR=5×10141073=15×107=1.5×108                  ∴μ=Cv=2V=\frac{w}{R}=\frac{5\times 10^{14}}{\frac{10^7}{3}}=15\times10^7=1.5\times 10^{8}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\therefore\mu=\frac{C}{v}=2
(3)(By0)=(Ey)0C=303×108=1×10−7(B_{y0})=\frac{(E_y)_0}{C}=\frac{30}{3\times10^{8}}=1\times10^{-7}
(4)(Bx0)=(Ex)0C=603×108=2×10−7(B_{x0})=\frac{(E_x)_0}{C}=\frac{60}{3\times10^{8}}=2\times10^{-7}