Import Question JSON

Current Question (ID: 20416)

Question:

$\text{A long straight wire with a circular cross-section having radius R is carrying a steady current I.}$ $\text{The current I is uniformly distributed across this cross-section.}$ $\text{Then the variation of the magnetic field due to the current I with distance r (r<R) from its centre will be:}$

Options:

1. $B \propto r^2$
2. $B \propto r$
3. $B \propto \frac{1}{r^2}$
4. $B \propto \frac{1}{r}$

Solution:

$\text{For a long straight wire with uniform current distribution,}$ $\text{the magnetic field inside the wire (r<R) is given by:}$ $B \propto r$

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
}