Import Question JSON

Current Question (ID: 16946)

Question:

$\text{A square loop with a side length of } 1 \text{ m and resistance of } 1 \, \Omega \text{ is placed in a uniform magnetic field of } 0.5 \, \text{T.}$ $\text{The plane of the loop is perpendicular to the direction of the magnetic field.}$ $\text{The magnetic flux through the loop is:}$

Options:

1. $\text{zero}$
2. $2 \, \text{Wb}$
3. $0.5 \, \text{Wb}$
4. $1 \, \text{Wb}$

Solution:

$\text{Hint: The magnetic flux through a loop, } \phi = \vec{B} \cdot \vec{A}$ $\text{Step: Find the value of the magnetic flux.}$ $\text{The magnetic flux through a loop is given by;} \Rightarrow \phi = \vec{B} \cdot \vec{A} = BA \cos \theta$ $\Rightarrow \phi = 0.5 \times 1^2 = 0.5 \text{ weber}$ $\text{Hence, option (3) is the correct answer.}$

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
}