Import Question JSON

Current Question (ID: 16754)

Question:

$\text{The magnetic induction at point } P, \text{ which is } 4 \text{ cm from a long current-carrying wire is } 10^{-8} \text{ Tesla.}$ $\text{What would be the field of induction at a distance of } 12 \text{ cm from the same current?}$

Options:

1. $3.33 \times 10^{-9} \text{ Tesla}$
2. $1.11 \times 10^{-4} \text{ Tesla}$
3. $3 \times 10^{-3} \text{ Tesla}$
4. $9 \times 10^{-2} \text{ Tesla}$

Solution:

$\text{B} = \frac{\mu_0}{4\pi} \frac{2i}{r} \Rightarrow \frac{B_1}{B_2} = \frac{r_2}{r_1} \Rightarrow \frac{10^{-8}}{B_2} = \frac{12}{4} \Rightarrow B_2 = 3.33 \times 10^{-9} \text{ Tesla}$

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
}