Import Question JSON

Current Question (ID: 16828)

Question:

$\text{A wire of length } l \text{ carrying current } i \text{ is folded to form a circular coil of } N \text{ turns.}$ $\text{What should be the value of } N \text{ to have the maximum value of the magnetic}$ $\text{moment in the coil?}$

Options:

1. $1$
2. $4$
3. $9$
4. $10$

Solution:

$\text{Step 1: Find the radius of coil}$ $\left(2\pi R\right)N = l$ $R = \frac{l}{2\pi N}$ $\text{Step 2: Find the magnetic moment of coil}$ $M = NIA$ $= NI\left(\pi R^2\right)$ $M = NI\pi\left(\frac{l}{2\pi N}\right)^2$ $= \frac{l^2}{4N\pi}$ $N = 1$

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
}