Import Question JSON

Current Question (ID: 16970)

Question:

$\text{A coil has } 1000 \text{ turns and } 500 \text{ cm}^2 \text{ as its area.}$ $\text{The plane of the coil is placed at right angles to a magnetic field of } 2 \times 10^{-5} \text{ Wb/m}^2.$ $\text{The coil is rotated through } 180^\circ \text{ in } 0.2 \text{ seconds.}$ $\text{The average emf induced in the coil, in milli-volts, is:}$

Options:

1. $5$
2. $10$
3. $15$
4. $20$

Solution:

$\text{The average emf } (\varepsilon) \text{ induced in the coil is given by Faraday's law:}$ $\varepsilon = -N \frac{\Delta \Phi}{\Delta t}$ $\text{where } N = 1000, \Delta t = 0.2 \text{ s, and } \Delta \Phi = B \cdot A \cdot \Delta \cos \theta.$ $\text{Given } B = 2 \times 10^{-5} \text{ Wb/m}^2, A = 500 \times 10^{-4} \text{ m}^2, \Delta \cos \theta = 2.$ $\varepsilon = -1000 \times \frac{2 \times 10^{-5} \times 500 \times 10^{-4} \times 2}{0.2}$ $= 10 \text{ mV}$

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
}