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Current Question (ID: 20671)

Question:

$\text{An electromagnetic wave is given as}$ $E = 200 \sin(1.5x - (4.5 \times 10^8)t)$, $\text{here } E \text{ is the electric field in } \text{N/C.}$ $\text{If energy density in the electromagnetic field is given as}$ $N \times 10^{-8} \text{ J/m}^3$. $\text{Then } N \text{ is: } (\varepsilon_0 = 9 \times 10^{-12} \text{ S.I units.})$

Options:

1. 9
2. 18
3. 36
4. 72

Solution:

$\text{Hint: Energy density in an electric field is } \mu_E = \frac{1}{2} \varepsilon_0 E^2$ $\varepsilon = \frac{1}{2} \varepsilon_0 E_{ms}^2 + \frac{B_{ms}^2}{2\mu_0}$ $= \varepsilon_0 E_{ms}^2 = \frac{1}{2} \varepsilon_0 E_0^2$ $= \frac{1}{2} \times 9 \times 10^{-12} \times 200 \times 200$ $= \frac{36}{2} \times 10^{-8} = 18 \times 10^{-8} \text{ J/m}^3$

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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
}