Import Question JSON

Current Question (ID: 20375)

Question:

$\text{An infinite wire is bent in the shape as shown in the figure with portion } AOB \text{ being semi-circular of radius } R. \text{ If current } i \text{ flows through the wire, then the magnetic field at the centre } O \text{ is equal to:}$

Options:

1. $\frac{\mu_0 i}{\pi R}$
2. $\frac{\mu_0 i}{2R}$
3. $\frac{\mu_0 i}{3R}$
4. $\frac{\mu_0 i}{4R}$

Solution:

$\text{Magnetic field due to section 1 and 3 of the wire will be zero as centre is in the line of the wire, therefore field will be due to section 2 only.}$ $\text{Thus, } B = \frac{\mu_0 i}{4\pi R} \times \pi = \frac{\mu_0 i}{4R}$

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
}