Import Question JSON

Current Question (ID: 20514)

Question:

$\text{Two coil } 'P' \text{ and } 'Q' \text{ are separated by some distance. When a current of } 3 \text{ A flows through coil } 'P' \text{ a magnetic flux of } 10^{-3} \text{ Wb passes through } 'Q'. \text{ No current is passed through } 'Q'. \text{ When no current passes through } 'P' \text{ and a current of } 2 \text{ A passes through } 'Q', \text{ the flux through } 'P' \text{ is:}$

Options:

1. $6.67 \times 10^{-3} \text{ Wb}$
2. $3.67 \times 10^{-4} \text{ Wb}$
3. $6.67 \times 10^{-4} \text{ Wb}$
4. $3.67 \times 10^{-3} \text{ Wb}$

Solution:

$\text{Hint: } \phi = BA$ $\phi = \frac{BA}{2(R^2 + x^2)^{3/2} \pi R^2} = 10^{-3}$ $\phi_Q = \frac{\mu_0 i_2 R^2}{2(r^2 + x^2)^{3/2} \pi R^2}$ $\frac{\phi_P}{\phi_Q} = \left(\frac{R^2 + x^2}{R^2 + x^2}\right)^{3/2} \phi_P = \frac{2}{3} \times 10^{-3} = 6.67$

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
}