Import Question JSON

Current Question (ID: 16986)

Question:

$\text{A rectangular, a square, a circular, and an elliptical loop, all in the } (x-y) \text{ plane,}$ $\text{are moving out of a uniform magnetic field with a constant velocity, } \vec{v} = v \hat{i}. $ $\text{The magnetic field is directed along the negative } z\text{-axis direction.}$ $\text{The induced emf, during the passage of these loops out of the field region,}$ $\text{will not remain constant for:}$

Options:

1. $\text{the rectangular, circular, and elliptical loops.}$
2. $\text{the circular and the elliptical loops.}$
3. $\text{only the elliptical loop.}$
4. $\text{any of the four loops.}$

Solution:

$\text{(2) Hint: The change in magnetic flux depends on the rate of change in the area.}$ $\text{Step 1: Find the rate of change in area in each case.}$ $\text{The area crossed per second for the magnetic field will not remain constant}$ $\text{for elliptical and circular loops, so the emf induced will not remain constant}$ $\text{for these loops.}$

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
}