Import Question JSON

Current Question (ID: 20353)

Question:

$\text{Magnitude of magnetic field (in SI units) at the centre of a hexagonal}$ $\text{shape coil of side 10 cm, 50 turns and carrying current } I \text{ (Ampere) in}$ $\text{units of } \frac{\mu_0 I}{\pi} \text{ is:}$

Options:

1. $5\sqrt{3}$
2. $250\sqrt{3}$
3. $50\sqrt{3}$
4. $500\sqrt{3}$

Solution:

$\text{Hint: } B = \frac{\mu_0 NI}{4\pi d} (\sin \theta_1 + \sin \theta_2)$ $r = a \cos 30^\circ$ $B = \frac{6\mu_0 I}{4\pi a \cos 30^\circ} \times 2 \sin 30^\circ \times 50$ $= \frac{\mu_0 I}{\pi} \frac{150}{\sqrt{3}a} = \frac{50\sqrt{3}}{0.1} \frac{\mu_0 I}{\pi}$ $= 500\sqrt{3} \frac{\mu_0 I}{\pi}$

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
}