Import Question JSON

Current Question (ID: 20100)

Question:

$\text{An electric field } \vec{E} = (2x\hat{i}) \text{ NC}^{-1} \text{ exists in space. A cube of side } 2 \text{ m is placed in the space as per figure given below. The electric flux through the cube is:}$

Options:

1. $0 \text{ Nm}^2/\text{C}$
2. $4 \text{ Nm}^2/\text{C}$
3. $8 \text{ Nm}^2/\text{C}$
4. $16 \text{ Nm}^2/\text{C}$

Solution:

$\text{The electric flux } \Phi \text{ through a closed surface is given by Gauss's law:}$ $\Phi = \oint \vec{E} \cdot d\vec{A}$ $\text{For a cube of side } 2 \text{ m, the surface area } A = 6 \times (2)^2 = 24 \text{ m}^2.$ $\text{The electric field } \vec{E} = (2x\hat{i}) \text{ NC}^{-1} \text{ varies with } x.$ $\text{The flux through the cube is } \Phi = \int_{0}^{2} (2x) \cdot 2 \text{ dx} = 16 \text{ Nm}^2/\text{C}.$

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
}