Import Question JSON

Current Question (ID: 16811)

Question:

$\text{The figure depicts a cross-section of a large metal sheet with an electric current flowing along its surface. The current in a } dl\text{-width strip is } (K dl), \text{ where } K \text{ is a constant. What is the magnetic field at a point } P \text{ and at a distance } x \text{ from the metal strips?}$

Options:

1. $\frac{1}{2} \mu_0 K x$
2. $\mu_0 K$
3. $\frac{1}{2} \mu_0 K$
4. $\frac{\mu_0 K x}{4}$

Solution:

$\text{Consider two strips A and C of the sheet situated symmetrically on the two sides of P. The resultant magnetic field at P will be parallel to the sheet.}$ $\text{From the ampere law for the rectangle shown in the figure.}$ $2B l = \mu_0 K l$ $\Rightarrow B = \frac{1}{2} \mu_0 K$

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
}