Import Question JSON

Current Question (ID: 17431)

Question:

$\text{In an electromagnetic wave in free space, the root mean square value of the electric field is } E_{\text{rms}} = 6 \text{ V/m. The peak value of the magnetic field is:}$

Options:

1. $2.83 \times 10^{-8} \text{ T}$
2. $0.70 \times 10^{-8} \text{ T}$
3. $4.23 \times 10^{-8} \text{ T}$
4. $1.41 \times 10^{-8} \text{ T}$

Solution:

$\text{Given, } E_{\text{rms}} = 6 \text{ V/m of an electromagnetic wave,}$ $\text{we know, } \frac{E_{\text{rms}}}{B_{\text{rms}}} = c$ $\text{so, } B_{\text{rms}} = \frac{E_{\text{rms}}}{c} \quad \ldots(1)$ $\text{we have, } B_{\text{rms}} = \frac{B_0}{\sqrt{2}}$ $B_0 = \sqrt{2} B_{\text{rms}}$ $\text{from equation 1}$ $B_0 = \sqrt{2} \times \frac{E_{\text{rms}}}{c}$ $B_0 = \sqrt{2} \times \frac{6}{3 \times 10^8} = 2.83 \times 10^{-8} \text{ T}$

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
}