Import Question JSON

Current Question (ID: 20035)

Question:

$\text{A charge } 'q' \text{ is placed at one corner of a cube as shown in figure. The flux of electrostatic field } \vec{E} \text{ through the shaded area is:}$

Options:

1. $\frac{q}{4\varepsilon_0}$
2. $\frac{q}{8\varepsilon_0}$
3. $\frac{24\varepsilon_0}{q}$
4. $\frac{48\varepsilon_0}{q}$

Solution:

$\phi = \int \vec{E} \cdot d\vec{a} = \frac{q}{\varepsilon_0}$ $\text{flux through cube} = \frac{q}{8\varepsilon_0}$ $\text{flux through surfaces ABEH, ADGH, ABCD will be zero}$ $\phi(\text{EFGH}) = \phi(\text{DCFG}) = \phi(\text{EBCF}) = \frac{1}{3} \left( \frac{q}{8\varepsilon_0} \right) = \frac{q}{24\varepsilon_0}$

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
}