Import Question JSON

Current Question (ID: 20371)

Question:

$\text{A current-carrying loop of radius } a \text{ is placed in the X-Y plane with its center at the origin. The magnetic field on the point } (0, 0, a) \text{ is:}$

Options:

1. $\frac{\mu_0 i}{2 \sqrt{2} a}$
2. $\frac{\mu_0 i}{4 \sqrt{2} a}$
3. $\frac{4 \sqrt{2} a}{2 \mu_0 i}$
4. $\frac{a}{\mu_0 i} \cdot \frac{1}{4a}$

Solution:

$\text{Hint: } \vec{B} = \frac{\mu_0}{4 \pi} \cdot \frac{2 \vec{\mu}}{(a^2 + z^2)^{3/2}}$ $\text{Magnetic moment: } |\vec{\mu}| = (\pi a^2) i$ $\vec{B} = \frac{\mu_0}{2} \cdot \frac{a^2 i}{(a^2 + z^2)^{3/2}}$ $\text{For } z = a:$ $\vec{B} = \frac{\mu_0}{2} \cdot \frac{a^2 i}{(2a^2)^{3/2}} = \frac{\mu_0 i}{4 \sqrt{2} a}$

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
}