Import Question JSON

Current Question (ID: 16481)

Question:

$\text{Four equal charges } Q \text{ are placed at the four corners of a square of each side } a. \text{ Work done in removing a charge } -Q \text{ from its centre to infinity is:}$

Options:

1. $0$
2. $\frac{\sqrt{2}Q^2}{4\pi\varepsilon_0 a}$
3. $\frac{\sqrt{2}Q^2}{\pi\varepsilon_0 a}$
4. $\frac{Q^2}{2\pi\varepsilon_0 a}$

Solution:

$\text{Hint: } W = \Delta U$ $\text{Step 1: Find initial P.E. of charge } -Q.$ $U_i = \frac{-4kQ^2\sqrt{2}}{a}$ $\text{Step 2: Find the final P.E. of charge } -Q.$ $U_f = 0$ $\text{Step 3: Find change in potential energy}$ $W = U_f - U_i = \frac{\sqrt{2}Q^2}{\pi\varepsilon_0 a}$

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
}