Import Question JSON

Current Question (ID: 16978)

Question:

$\text{In the figure shown a square loop } P Q R S \text{ of side } a \text{ and resistance } r \text{ is placed near an infinitely long wire carrying a constant current } I. \text{ The sides } P Q \text{ and } R S \text{ are parallel to the wire. The wire and the loop are in the same plane. The loop is rotated by } 180^\circ \text{ about an axis parallel to the long wire and passing through the midpoints of the side } Q R \text{ and } P S. \text{ The total amount of charge which passes through any point of the loop during rotation is:}$

Options:

1. $\frac{\mu_0 I a}{2 \pi r} \ln(2)$
2. $\frac{\mu_0 I a}{\pi r} \ln(2)$
3. $\frac{\mu_0 I a^2}{2 \pi r}$
4. $\text{cannot be found because the time of rotation not given.}$

Solution:

$\text{(2)}$ $\text{dq} = \frac{-d\phi}{R}$ $= \frac{2 \phi_i}{R} = \frac{2 \mu_0 I a}{R \cdot 2 \pi} \ln \left( \frac{2a}{a} \right) = \frac{\mu_0 I a \cdot \ln(2)}{\pi R}$

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
}