Import Question JSON

Current Question (ID: 20372)

Question:

$\text{A current } 2 \text{ A is flowing through the sides of an equilateral triangular loop of side } 4\sqrt{3} \text{ m as shown. The magnetic field induction at the centroid of the triangle is:}$

Options:

1. $3\sqrt{3} \times 10^{-7} \text{ T}$
2. $\sqrt{3} \times 10^{-7} \text{ T}$
3. $2\sqrt{3} \times 10^{-7} \text{ T}$
4. $5\sqrt{3} \times 10^{-7} \text{ T}$

Solution:

$\frac{r}{2\sqrt{3}} = \tan 30^\circ$ $r = 2 \text{ m}$ $\text{Magnetic field at centroid}$ $B = 3 \times \frac{\mu_0 I}{4\pi r} \left( \sin 60^\circ + \sin 60^\circ \right)$ $= 3 \times \frac{\mu_0 \times 2}{4\pi \times 2} \left( \frac{\sqrt{3}}{2} + \frac{\sqrt{3}}{2} \right) = 3\sqrt{3} \times 10^{-7} \text{ T}$

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
}