Import Question JSON

Current Question (ID: 20626)

Question:

$\text{An electromagnetic wave traveling in the } x\text{-direction has the frequency of } 2 \times 10^{14} \text{ Hz and electric field amplitude of } 27 \text{ Vm}^{-1}. \text{ From the options given below, which one describes the magnetic field for this wave?}$

Options:

1. $\vec{B}(x,t) = (9 \times 10^{-8} \text{ T}) \hat{j} \sin [1.5 \times 10^{-6} x - 2 \times 10^{14} t]$
2. $\vec{B}(x,t) = (9 \times 10^{-8} \text{ T}) \hat{i} \sin [2\pi (1.5 \times 10^{-8} x - 2 \times 10^{14} t)]$
3. $\vec{B}(x,t) = (9 \times 10^{-8} \text{ T}) \hat{k} \sin [2\pi (1.5 \times 10^{-6} x - 2 \times 10^{14} t)]$
4. $\vec{B}(x,t) = (3 \times 10^{-8} \text{ T}) \hat{j} \sin [2\pi (1.5 \times 10^{-8} x - 2 \times 10^{14} t)]$

Solution:

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

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
}