Import Question JSON

Current Question (ID: 20387)

Question:

$\text{Two rings of equal radius } R \text{ arranged perpendicular to each other with a common centre at } C, \text{ carrying equal current } I. \text{ Then the magnetic field at the common centre } C \text{ is:}$

Options:

1. $\frac{\mu_0 I}{2R}$
2. $\frac{\mu_0 I}{R}$
3. $\frac{\sqrt{2} \mu_0 I}{R}$
4. $\frac{\mu_0 I}{\sqrt{2} R}$

Solution:

$\text{Hint: } B_c = \frac{\mu_0 I}{2R}$ $\vec{B}_1 = \frac{\mu_0 I}{2R} \hat{i}, \vec{B}_2 = \frac{\mu_0 I}{2R} \hat{j}$ $B_C = \frac{\mu_0 I}{\sqrt{2} R}$

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
}