Import Question JSON

Current Question (ID: 16949)

Question:

$\text{A coil having number of turns } N \text{ and cross-sectional area } A \text{ is rotated in a uniform magnetic field } B \text{ with an angular velocity } \omega. \text{ The maximum value of the emf induced in it is:}$

Options:

1. $\frac{NBA}{\omega}$
2. $NBA\omega$
3. $\frac{NBA}{\omega^2}$
4. $NBA\omega^2$

Solution:

$\text{The flux linking with the coil at any instant } t \text{ is given as } \Phi = NBA \cos \omega t$ $\therefore \varepsilon = -\frac{d\Phi}{dt} = NBA\omega \sin \omega t$ $\text{Therefore, the maximum value of emf is } \varepsilon_{\text{max}} = NBA\omega$

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
}