Import Question JSON

Current Question (ID: 16758)

Question:

$\text{In the figure shown below there are two semicircles of radius } r_1 \text{ and } r_2 \text{ in which a current } i \text{ is flowing. The magnetic induction at the centre of } O \text{ will be:}$

Options:

1. $\frac{\mu_0 i}{r \left( r_1 + r_2 \right)}$
2. $\frac{\mu_0 i}{4} \left[ \frac{r_1 + r_2}{r_1 r_2} \right]$
3. $\frac{\mu_0 i}{4 \left( r_1 - r_2 \right)}$
4. $\frac{\mu_0 i}{4} \left[ \frac{r_2 - r_1}{r_1 r_2} \right]$

Solution:

$\text{(b) The magnetic induction due to both semicircular parts will be in the same direction perpendicular to the paper inwards.}$ $\therefore \text{B} = \text{B}_1 + \text{B}_2 = \frac{\mu_0 i}{4 r_1} + \frac{\mu_0 i}{4 r_2} = \frac{\mu_0 i}{4} \left( \frac{r_1 + r_2}{r_1 r_2} \right) \otimes$

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
}