Import Question JSON

Current Question (ID: 16944)

Question:

$\text{A square of side } L \text{ meters lies in the } XY\text{-plane in a region where the magnetic field is given by } \vec{B} = B_0 \left( 2\hat{i} + 3\hat{j} + 4\hat{k} \right) \text{ T where } B_0 \text{ is constant. The magnitude of flux passing through the square will be:}$

Options:

1. $2B_0L^2 \text{ Wb}$
2. $3B_0L^2 \text{ Wb}$
3. $4B_0L^2 \text{ Wb}$
4. $\sqrt{29}B_0L^2 \text{ Wb}$

Solution:

$\text{Hint: } \phi = \vec{B} \cdot \vec{A}$ $\text{Step 1: Find the flux.}$ $\text{Here,}$ $\vec{A} = L^2\hat{k} \text{ and } \vec{B} = B_0 \left( 2\hat{i} + 3\hat{j} + 4\hat{k} \right) \text{ T}$ $\phi = \vec{B} \cdot \vec{A} = B_0 \left( 2\hat{i} + 3\hat{j} + 4\hat{k} \right) \cdot L^2\hat{k} = 4B_0L^2 \text{ Wb}$

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
}