Import Question JSON

Current Question (ID: 20049)

Question:

$\text{A charge } q \text{ is placed at the centre of the bottom face of a cuboid, as shown in the diagram.}$ $\text{What is the electric flux through the shaded surface?}$

Options:

1. $\frac{2q}{7\varepsilon_0}$
2. $\frac{q}{12\varepsilon_0}$
3. $\frac{q}{4\varepsilon_0}$
4. $\frac{q}{6\varepsilon_0}$

Solution:

$\text{Hint: Apply Gauss's law.}$ $\text{Step: Find the electric flux through the shaded surface.}$ $\text{Place a similar box at the bottom as shown in the figure below;}$$\text{We get a cube of side } 2L. \text{ The charge } q \text{ is then at the centre of the new cube.}$ $\text{By applying Gauss's law;}$$\phi = \int \vec{E} \cdot d\vec{A} = \frac{q_{\text{enclosed}}}{\varepsilon_0}$$\text{From one surface of the cube, the electric flux given by;}$$\phi = \frac{1}{6} \left( \frac{q_{\text{enclosed}}}{\varepsilon_0} \right)$$\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
}