Import Question JSON

Current Question (ID: 20425)

Question:

$\text{Two long current-carrying conductors are placed parallel to each other at a distance of } 8 \text{ cm between them.}$ $\text{The magnitude of the magnetic field produced at the mid-point between the two conductors due to the current flowing in them is } 300 \, \mu\text{T.}$ $\text{The equal current flowing in the two conductors is:}$

Options:

1. $30 \, \text{A in the same direction}$
2. $30 \, \text{A in the opposite direction}$
3. $60 \, \text{A in the opposite direction}$
4. $300 \, \text{A in the opposite direction}$

Solution:

$\text{The magnetic field at the midpoint due to each conductor is given by } B = \frac{\mu_0 I}{2 \pi d}.$ $\text{For two conductors carrying current in opposite directions, the fields add up:}$ $2B = 300 \, \mu\text{T} \Rightarrow B = 150 \, \mu\text{T}.$ $\text{Using } B = \frac{\mu_0 I}{2 \pi d}, \text{ we find } I = 30 \, \text{A}.$

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
}