Import Question JSON

Current Question (ID: 20646)

Question:

$\text{The electric field in an electromagnetic wave is given by}$ $E = 56.5 \sin \omega (t - \frac{x}{c}) \text{ NC}^{-1}.$ $\text{The intensity of the wave if it is propagating along the } x\text{-axis in the free space is: (Given:}$ $\varepsilon_0 = 8.85 \times 10^{-12} \text{ C}^2\text{N}^{-1}\text{m}^{-2})$

Options:

1. $5.65 \text{ Wm}^{-2}$
2. $4.24 \text{ Wm}^{-2}$
3. $1.9 \times 10^{-7} \text{ Wm}^{-2}$
4. $56.5 \text{ Wm}^{-2}$

Solution:

$\text{Hint: } I = \frac{1}{2} \varepsilon_0 E^2 c$

Import JSON File

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
}