Import Question JSON

Current Question (ID: 20358)

Question:

$\text{A square loop of side } 2a, \text{ and carrying current } I, \text{ is kept in } XZ \text{ plane}$ $\text{with its centre at origin. A long wire carrying the same current } I \text{ is}$ $\text{placed parallel to the } z\text{-axis and passing through the point } (0, b, 0), (b \gg a).$ $\text{The magnitude of the torque on the loop about } z\text{-axis is given by:}$

Options:

1. $\frac{2\mu_0 I^2 a^2}{\pi b}$
2. $\frac{\pi b}{\mu_0 I^2 a^3}$
3. $\frac{2\pi b^2}{\mu_0 I^2 a^3}$
4. $\frac{2\pi b}{\pi b^2}$

Solution:

$\text{Hint: } \vec{\tau} = \vec{M} \times \vec{B}$ $\vec{\tau} = \vec{M} \times \vec{B}$ $= 4a^2 I \times \frac{\mu_0 I}{2\pi b}$

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
}