1. Calculation of the Speed of Light in a Medium:

- The speed of light in a medium, denoted as $$ V $$, is given by the formula $$ V = \frac{W}{k} $$.

- Substituting values, we get $$ V = \frac{3 \times 5 \times 10^{14}}{10^7} = 1.5 \times 10^8 \text{ m/s} $$.

2. Determination of the Refractive Index:

- The refractive index, $$ \mu $$, is the ratio of the speed of light in vacuum, $$ C $$, to the speed of light in the medium, $$ V $$.

- Substituting values, $$ \mu = \frac{3 \times 10^8}{1.5 \times 10^8} = 2 $$.

- Hence, the refractive index $$ \mu $$ is 2.

Therefore, the option (D) is the answer.

Given, $\vec{E}=30(2 \hat{x}+\hat{y}) \sin \left[2 \pi\left(5 \times 10^{14} t-\frac{10^7}{3} z\right)\right] \mathrm{Vm}^{-1}$

Now magnitude of

$$ \begin{aligned} B & =\frac{E}{v} \\\\ \Rightarrow B & =\frac{30 \sqrt{5}}{1.5 \times 10^8} \end{aligned} $$

JEE Advanced 2023 Paper 2 Online Physics - Electromagnetic Waves Question 1 English Explanation

JEE Advanced 2023 Paper 2 Online Physics - Electromagnetic Waves Question 1 English Explanation

$\begin{aligned} & \tan \alpha=\frac{1}{2} \\\\ & \sin \alpha=\frac{1}{\sqrt{5}}\end{aligned}$

The direction of $\vec{B}$ is along the direction of $\vec{v} \times \vec{E}$

i.e. $\hat{v} \times \hat{E}=\hat{B}$

Now $ B_x=-B \sin \alpha$

$$ \Rightarrow B_x=-\frac{30 \sqrt{5}}{1.5 \times 10^8} \times \frac{1}{\sqrt{5}}=-2 \times 10^7 $$

Therefore, option (A) is the answer.

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Electromagnetic Waves · Physics · JEE Advanced

MCQ (More than One Correct Answer)