Import Question JSON

Current Question (ID: 20377)

Question:

$\text{Two identical current carrying coils with same centre are placed with their planes perpendicular to each other as shown.}$ $\text{If } i = \sqrt{2} A \text{ and radius of coils is } R = 1 \text{ m then magnetic field at centre C is equal to:}$

Options:

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

Solution:

$\text{Hint: } B = \frac{\mu_0 i}{2r}$ $i = \sqrt{2} A$ $B_{\text{net}} = \sqrt{B_1^2 + B_2^2}$ $= \sqrt{\left(\frac{\mu_0 i}{2R}\right)^2 + \left(\frac{\mu_0 i}{2R}\right)^2}$ $= \mu_0$

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
}