Import Question JSON

Current Question (ID: 16942)

Question:

$\text{If a current is passed through a circular loop of radius } R \text{ then magnetic flux through a coplanar square loop of side } l \text{ as shown in the figure } (l \ll R) \text{ is:}$

Options:

1. $\frac{\mu_0 I}{2} \frac{R^2}{l}$
2. $\frac{\mu_0 I l^2}{2R}$
3. $\frac{2R}{\mu_0 I \pi R^2}$
4. $\frac{2l}{\mu_0 \pi R^2 I}$

Solution:

$\text{Hint: } \phi = BA \cos \theta$ $\text{Step: Find the magnetic flux through a coplanar square loop of side } l$ $\text{The magnetic flux through a coplanar square loop of side } l \text{ is given by:}$ $\phi = BA \cos \theta$ $\text{The magnetic field is given by:}$ $B = \frac{\mu_0}{2} \frac{I}{R}$ $\therefore \phi = BA \cos \theta = \frac{\mu_0}{2} \frac{I}{R} \times l^2 (\cos 0^\circ)$ $\Rightarrow \phi = \frac{\mu_0 I l^2}{2R}$ $\text{Hence, option (2) is the correct answer.}$

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
}