Import Question JSON

Current Question (ID: 20097)

Question:

$\sigma$ \text{ is the uniform surface charge density of a thin spherical shell of radius } R. \text{ The electric field at any point on the surface of the spherical shell is:}

Options:

1. $\frac{\sigma}{\varepsilon_0} R$
2. $\frac{\sigma}{\varepsilon_0}$
3. $\frac{\sigma}{2\varepsilon_0}$
4. $\frac{\sigma}{4\varepsilon_0}$

Solution:

$\text{The electric field on the surface of a charged spherical shell is given by Gauss's law:}$ $E = \frac{\sigma}{\varepsilon_0}$ $\text{where } \sigma \text{ is the surface charge density and } \varepsilon_0 \text{ is the permittivity of free space.}$

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
}