Import Question JSON

Current Question (ID: 16972)

Question:

$\text{A coil of a mean area of } 500 \text{ cm}^2 \text{ and } 1000 \text{ turns is held perpendicular to a uniform field of } 0.4 \text{ Gauss.}$ $\text{The coil is turned through } 180^\circ \text{ in } \frac{1}{10} \text{ seconds.}$ $\text{The average induced emf is:}$

Options:

1. $0.04 \text{ V}$
2. $0.4 \text{ V}$
3. $4 \text{ V}$
4. $0.004 \text{ V}$

Solution:

$\text{Hint: } \varepsilon_{\text{ind}} = \frac{\Delta \phi}{t}$ $\text{Step: Find the average induced emf.}$ $\text{The average magnetic flux linked with the coil is given by:}$ $\phi = NBA$ $\text{The change in magnetic flux is given by:}$ $\Delta \phi = 2NBA$ $\text{The average induced emf is given by:}$ $\varepsilon_{\text{ind}} = \frac{\Delta \phi}{t}$ $\Rightarrow \varepsilon_{\text{ind}} = \frac{2NBA}{t} = \frac{2 \times 1000 \times 0.4 \times 10^{-4} \times 500 \times 10^{-4}}{0.1}$ $\Rightarrow \varepsilon_{\text{ind}} = 0.04 \text{ V}$ $\text{Hence, option (1) is the correct answer.}$

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
}