Import Question JSON

Current Question (ID: 20642)

Question:

$\vec{E} = E_0 (\hat{x} + \hat{y}) \sin(kz - \omega t).$ $\text{Its magnetic field will be given by:}$

Options:

1. $\frac{E_0}{c} (-\hat{x} + \hat{y}) \sin(kz - \omega t)$
2. $\frac{E_0}{c} (\hat{x} + \hat{y}) \sin(kz - \omega t)$
3. $\frac{E_0}{c} (\hat{x} - \hat{y}) \sin(kz - \omega t)$
4. $\frac{E_0}{c} (-\hat{x} - \hat{y}) \sin(kz - \omega t)$

Solution:

$\text{Hint: Electric and magnetic fields are perpendicular to each other.}$ $\vec{E} = E_0 (\hat{x} + \hat{y}) \sin(kz - \omega t)$ $\text{direction of propagation} = + \hat{k}$ $\hat{k} = \frac{\hat{i} + \hat{j}}{\sqrt{2}} \times \hat{B} \Rightarrow \hat{B} = \frac{-\hat{i} + \hat{j}}{\sqrt{2}}$ $\therefore \vec{B} = \frac{E_0}{c} (-\hat{x} + \hat{y}) \sin(kz - \omega t)$

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
}