Import Question JSON

Current Question (ID: 16823)

Question:

$\text{A wire of length } L \text{ meters carrying a current of } I \text{ ampere is bent in the form of a circle. What is its magnetic moment?}$

Options:

1. $\frac{IL^2}{4} \text{ A-m}^2$
2. $\frac{I \times \pi L^2}{4} \text{ A-m}^2$
3. $\frac{2IL^2}{\pi} \text{ A-m}^2$
4. $\frac{IL^2}{4\pi} \text{ A-m}^2$

Solution:

$\text{Hint: Use the formula of the magnetic moment.}$ $\text{Step: Find the magnetic moment of the loop.}$ $\text{The radius of the circular loop is given by:}$ $2\pi r = L$ $r = \frac{L}{2\pi}$ $\text{The magnetic moment of the loop is given by:}$ $M = I \times A$ $M = I \left( \pi r^2 \right)$ $M = I \times \left( \pi \right) \times \left( \frac{L}{2\pi} \right)^2$ $\Rightarrow M = \frac{L^2}{4\pi}$ $\text{Hence, option (4) is the correct answer.}$

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
}