Import Question JSON

Current Question (ID: 16498)

Question:

$\text{A thin spherical conducting shell of radius } R \text{ has a charge } q. \text{ Another charge } Q \text{ is placed at the centre of the shell. The electrostatic potential at a point } P \text{ which is at a distance } \frac{R}{2} \text{ from the centre of the shell is:}$

Options:

1. $\frac{(q+Q)}{4\pi\varepsilon_0} \frac{2}{R}$
2. $\frac{2Q}{4\pi\varepsilon_0 R}$
3. $\frac{2Q}{4\pi\varepsilon_0 R} - \frac{2q}{4\pi\varepsilon_0 R}$
4. $\frac{2Q}{4\pi\varepsilon_0 R} + \frac{q}{4\pi\varepsilon_0 R}$

Solution:

$\text{Electric potential due to a thin shell remains constant inside it and is equal to } \frac{Kq}{R}.$ $\text{Electric potential at } P = \text{potential due the charge } Q + \text{potential due to the shell}$ $V = \frac{kQ}{R/2} + \frac{kq}{R}$ $= \frac{2Q}{4\pi\varepsilon_0 R} + \frac{q}{4\pi\varepsilon_0 R}$

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
}