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Current Question (ID: 20631)

Question:

$\text{A monochromatic beam of light has a frequency } v = \frac{3}{2\pi} \times 10^{12} \text{ Hz}$ $\text{and is propagating along the direction } \frac{\hat{i} + \hat{j}}{\sqrt{2}}$ $\text{It is polarized along the } \hat{k}$ $\text{direction. The acceptable form of the magnetic field is:}$

Options:

1. $\frac{E_0}{C} \left( \frac{\hat{i} - \hat{j}}{\sqrt{2}} \right) \cos \left[ 10^4 \left( \frac{\hat{i} - \hat{j}}{\sqrt{2}} \right) \cdot \vec{r} - (3 \times 10^{12})t \right]$
2. $\frac{E_0}{C} \hat{k} \cos \left[ 10^4 \left( \frac{\hat{i} + \hat{j}}{\sqrt{2}} \right) \cdot \vec{r} + (3 \times 10^{12})t \right]$
3. $\frac{E_0}{C} \left( \frac{\hat{i} - \hat{j}}{\sqrt{2}} \right) \cos \left[ 10^4 \left( \frac{\hat{i} + \hat{j}}{\sqrt{2}} \right) \cdot \vec{r} + (3 \times 10^{12})t \right]$
4. $\frac{E_0}{C} \left( \frac{\hat{i} + \hat{j} + \hat{k}}{\sqrt{3}} \right) \cos \left[ 10^4 \left( \frac{\hat{i} + \hat{j}}{\sqrt{2}} \right) \cdot \vec{r} + (3 \times 10^{12})t \right]$

Solution:

$\text{Hint: } \frac{E_0}{B_0} = c$

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Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}