Import Question JSON

Current Question (ID: 20644)

Question:

$\text{A plane electromagnetic wave travels in a medium with relative}$ $\text{permeability } 1.61 \text{ and relative permittivity } 6.44. \text{ If the magnitude of}$ $\text{magnetic intensity is } 4.5 \times 10^{-2} \text{ Am}^{-1} \text{ at a point, the approximate}$ $\text{magnitude of electric field intensity at that point will be:}$ $\text{(Given: permeability of free space, } \mu_0 = 4\pi \times 10^{-7} \text{ NA}^{-2}, \text{ speed of}$ $\text{light in vacuum, } c = 3 \times 10^8 \text{ ms}^{-1})$

Options:

1. $16.96 \text{ Vm}^{-1}$
2. $2.25 \times 10^{-2} \text{ Vm}^{-1}$
3. $8.48 \text{ Vm}^{-1}$
4. $6.75 \times 10^6 \text{ Vm}^{-1}$

Solution:

$\text{Hint: } E = \frac{c}{n} \times B$ $\text{where } n = \sqrt{\mu_r \epsilon_r}$ $\text{and } B = 4.5 \times 10^{-2} \text{ Am}^{-1}$ $\text{Calculate } n = \sqrt{1.61 \times 6.44}$ $\text{Then } E = \frac{3 \times 10^8}{n} \times 4.5 \times 10^{-2}$

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
}