Import Question JSON

Current Question (ID: 20531)

Question:

$\text{A circular ring is placed in a magnetic field of } 0.4 \text{ T. Suddenly its radius starts shrinking at the rate of } 1 \text{ mm/s. What will be the induced EMF in the ring at } r = 2 \text{ cm?}$

Options:

1. $16\pi \ \mu\text{V}$
2. $8\pi \ \mu\text{V}$
3. $16\pi \ \text{mV}$
4. $8\pi \ \text{mV}$

Solution:

$\text{Hint: } \phi = BA$ $\text{Step: Find the induced emf in the ring.}$ $\text{The magnetic flux through the ring is given by:}$ $\phi = BA = \pi r^2 B$ $\text{The induced EMF through the ring is given by:}$ $E_{\text{induced}} = -\frac{d\phi}{dt}$ $\Rightarrow E_{\text{induced}} = -B \frac{d(\pi r^2)}{dt} = -2\pi Br \left( -\frac{dr}{dt} \right) = 2\pi Br \left( \frac{dr}{dt} \right)$ $\Rightarrow E_{\text{induced}} = 2\pi \times 0.4 \times 2 \times 10^{-2} \times 10^{-3} = 16\pi \times 10^{-6} \text{ V}$ $\text{Hence, option (1) is the correct answer.}$

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
}