Import Question JSON

Current Question (ID: 20431)

Question:

$B_X$ and $B_Y$ are the magnetic field at the centre of two coils of two coils $X$ and $Y$ respectively, each carrying equal current. If coil $X$ has 200 turns and 20 \text{ cm} radius and coil $Y$ has 400 turns and 20 \text{ cm} radius, the ratio of $B_X$ and $B_Y$ is:

Options:

1. 1: 1
2. 1: 2
3. 2: 1
4. 4: 1

Solution:

$B = \frac{\mu_0 n I}{2R}$ $\text{For coil } X: B_X = \frac{\mu_0 \times 200 \times I}{2 \times 20}$ $\text{For coil } Y: B_Y = \frac{\mu_0 \times 400 \times I}{2 \times 20}$ $\text{Ratio: } \frac{B_X}{B_Y} = \frac{200}{400} = \frac{1}{2}$

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
}