Import Question JSON

Current Question (ID: 17019)

Question:

$\text{The magnetic energy stored in a long solenoid of an area of cross-section } A \text{ in a small region of length } L \text{ is:}$

Options:

1. $\frac{B^2 AL}{2\mu_0^2}$
2. $\frac{AL}{2\mu_0}$
3. $\frac{1}{2\mu_0} B^2 AL$
4. $\frac{B^2 AL}{2\mu_0}$

Solution:

$\text{The magnetic energy stored in a solenoid is given by } U = \frac{1}{2} \frac{B^2}{\mu_0} \times \text{Volume}$ $\text{For a small region of length } L, \text{ Volume } = AL$ $\therefore U = \frac{1}{2} \frac{B^2}{\mu_0} \times AL = \frac{B^2 AL}{2\mu_0}$

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
}