Import Question JSON

Current Question (ID: 20053)

Question:

$\text{The electric field in a region is } \vec{E} = 2x^2 \hat{i} - 4y \hat{j} + 6z \hat{k}. \text{ What is the charge inside the cuboid shown below?}$

Options:

1. $-8\varepsilon_0$
2. $36\varepsilon_0$
3. $12\varepsilon_0$
4. $24\varepsilon_0$

Solution:

$\text{Hint: } \phi = \frac{q}{\varepsilon_0}$ $\text{Step 1: Find the net flux through the cuboid.}$ $\phi = \Rightarrow \phi = 24$ $\text{Step 2: Find the charge inside the cuboid.}$ $\text{By using Gauss's Law;} \frac{q}{\varepsilon_0} = 24$ $\Rightarrow q = 24\varepsilon_0$ $\text{Hence, option (4) is the correct answer.}$

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
}