Question

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $\vec{E}$=30(2𝑥̂ + 𝑦̂)sin [2𝜋 (5×1014𝑡 −$\frac{10^7}{3}z$)] Vm−1. Which of the following option(s) is(are) correct? [Given: The speed of light in vacuum, 𝑐 = 3 × 108 ms−1]

• A. 𝐵𝑥 = −2 × 10−7 sin [2𝜋(5×1014𝑡−$\frac{10^7}{3}z$)]Wb−2
• B. 𝐵y=2×10−7 sin[2𝜋(5×1014𝑡−$\frac{10^7}{3}z$)]Wb−2
• C. The wave is polarized in the 𝑥𝑦-plane with a polarization angle 30° with respect to the 𝑥-axis.
• D. The refractive index of the medium is 2

Answer 1

Answer: (A), (D)

𝐵𝑥 = −2 × 10−7 sin [2𝜋(5×1014𝑡−$\frac{10^7}{3}z$)]Wb−2

Answer 2

the speed of light in a medium is V=$\frac{w}{k}$
$v=\frac{3\times5\times10^{14}}{10^7}$
$v=1.5\times10^8$
refractive index = $\mu$ = $\frac{C}{V}=\frac{3\times10^8}{1.5\times10^8}=2$
$\mu=2$
given, $\vec{E}=30(2\hat{x}+\hat{y})\,sin(2\pi(5\times10^{14}-\frac{10^7}{3}))^\frac{1}{m}$

$B_0=\frac{E_0}{V}=\frac{30\sqrt{5}}{1.5\times10^8}$
Direction of $\vec{B_0}$ is ($\vec{V}\times\vec{E}$)
$\vec{V}\times\vec{E}=\hat{k}\times\frac{2\hat{i}+\hat{j}}{\sqrt5}$
$(\frac{-\hat{i}+2\hat{j}}{\sqrt5})$ put value $\vec{B_0}$ = $\frac{30\sqrt5}{1.5\times10^8}\times(\frac{-\hat{i}+2\hat{j}}{\sqrt5})$
$B_x=-2\times10^7$