Import Question JSON

Current Question (ID: 20370)

Question:

$\text{Point } O \text{ and two long wires are kept in the same plane such that point } O \text{ lies in the middle of the line. The magnetic field at point } O \text{ due to the current } i \text{ flowing in both the wires is equal to:}$

Options:

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

Solution:

$\text{Hint: } B = \frac{\mu_0 i}{4 \pi r}$ $\text{Magnetic field due to Wire section (1) and (3) shown in figure will not generate a field at } O.$ $\text{Magnetic field due to Wire section (2) and (4) will be equal to:}$ $B = 2 \times \frac{\mu_0 i}{4 \pi \left( \frac{l}{2} \right)} \left( \hat{k} \right) = \frac{\mu_0 i}{\pi l} \left( \hat{k} \right)$

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
}