Import Question JSON

Current Question (ID: 20667)

Question:

$\text{If electric field } (\vec{E}) \text{ at an instant is } 6.6 \text{ N/C } \hat{j} \text{ and the EM wave is}$ $\text{propagating along positive x-direction then B at that instant is given}$ $\text{by:}$

Options:

1. $2.2 \times 10^{-8} \hat{k} \text{T}$
2. $-2.2 \times 10^{8} \hat{k} \text{T}$
3. $-0.5 \times 10^{8} \hat{k} \text{T}$
4. $19.8 \times 10^{8} \hat{k} \text{T}$

Solution:

$\text{Hint: } \vec{v} = \vec{E} \times \vec{B}$ $\frac{\vec{E}}{\vec{B}} = C$ $\frac{\vec{B}}{\vec{E}} = \frac{6.6}{3 \times 10^{8}} = 2.2 \times 10^{-8} \text{T}$ $\text{Also } \hat{E} \times \hat{B} = \hat{C}$

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
}