Import Question JSON

Current Question (ID: 20378)

Question:

$\text{The given figure shows a long cylindrical shell having current } I \text{ flowing uniformly along the wall.}$ $\text{The graph showing the variation of magnetic field } (B) \text{ with the perpendicular distance } (r) \text{ from the axis of the shell is}$

Options:

1. $B \uparrow \text{ vs } r \text{ with a peak at } r = R$
2. $B \uparrow \text{ vs } r \text{ decreasing after } r = R$
3. $B \uparrow \text{ vs } r \text{ constant until } r = R \text{ then decreasing}$
4. $B \uparrow \text{ vs } r \text{ with a peak at } r = R \text{ and symmetric}$

Solution:

$\text{Hint: Use Ampere's circuital law.}$ $B_{\text{inside}} = 0$ $B_{\text{outside}} = \frac{\mu \cdot i}{2 \pi r}$ $\therefore \ B_{\text{outside}} \propto \frac{1}{r}$

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
}