Import Question JSON

Current Question (ID: 20438)

Question:

$\text{A solenoid of length } 2 \text{ m, has } 1200 \text{ turns. The magnetic field inside the solenoid, when } 2 \text{ A current is passed through it is:}$ $\text{(Diameter of the solenoid is } 0.5 \text{ m)}$

Options:

1. $48\pi \times 10^{-5} \text{ T}$
2. $48\pi \times 10^{-3} \text{ T}$
3. $48 \times 10^{-5} \text{ T}$
4. $36\pi \times 10^{-4} \text{ T}$

Solution:

$\text{Magnetic field inside solenoid } = \mu_0 ni$ $\text{where } n = \text{Number of turns per unit length } = \frac{1200}{2} = 600 \text{ turns/m}$ $B_{\text{solenoid}} = \mu_0 ni = (4\pi \times 10^{-7} \times 600 \times 2) \text{ T}$ $= 8\pi \times 10^{-7} \times 600 \text{ T} = 48\pi \times 10^{-5} \text{ T}$

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
}