Import Question JSON

Current Question (ID: 20403)

Question:

$\text{The magnitude of the magnetic field at the centre of an equilateral}$ $\text{triangular loop of side 1 m which is carrying a current of 10 A is:}$ $\text{[Take } \mu_0 = 4\pi \times 10^{-7} \text{ NA}^{-2}]$

Options:

1. $3 \, \mu\text{T}$
2. $18 \, \mu\text{T}$
3. $9 \, \mu\text{T}$
4. $1 \, \mu\text{T}$

Solution:

$\text{Hint: } B = 3 \left[ \frac{\mu_0 i}{4\pi} (\sin 60^\circ + \sin 60^\circ) \right]$ $B = \frac{3 \mu_0 i}{\pi a} \sin \frac{\pi}{3} \tan \frac{\pi}{3}$ $= \frac{9 \mu_0 i}{2 \pi a}$ $= \frac{9}{2 \pi} \times 4\pi \times 10^{-7} \times 10$ $= 18 \times 10^{-6} \, \text{T}$

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
}