Import Question JSON

Current Question (ID: 17418)

Question:

$\text{An EM wave is propagating in a medium with a velocity } \vec{v} = v \hat{i}. \text{ The instantaneous oscillating electric field of this EM wave is along the } +y \text{ axis.}$ $\text{The direction of the oscillating magnetic field of the EM wave will be along:}$

Options:

1. $-z\text{-direction}$
2. $+z\text{-direction}$
3. $-y\text{-direction}$
4. $+y\text{-direction}$

Solution:

$\text{As we know } \vec{V} = \vec{E} \times \vec{B} \text{ or } \hat{i} = \hat{j} \times \hat{k}$ $\text{Direction of propagation in } \hat{i} \text{ (x-direction) and } \vec{E} \text{ is given in } \hat{j} \text{ direction } (\hat{j}).$ $\text{So from right-hand thumb rule, B is in + z-direction}$ $\therefore \vec{B} = \hat{k}$

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
}