Import Question JSON

Current Question (ID: 16586)

Question:

$\text{Surface charge density on the positive plate of a charged parallel plate capacitor is } \sigma. \text{ Energy density in the electric field of the capacitor is:}$

Options:

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

Solution:

$\text{Hint: The energy density = energy per unit volume.}$ $\text{Step 1: Find the energy stored between capacitors.}$ $\text{E} = \frac{Q^2}{2C} = \frac{(\sigma A)^2 d}{2A\varepsilon_0} = \frac{\sigma^2 (Ad)}{2\varepsilon_0}$ $\text{E} = \frac{\sigma^2}{2\varepsilon_0}$ $\text{Step 2: Find the energy density}$ $\text{E.D.} = \frac{\sigma^2}{2\varepsilon_0} = \frac{E}{V}$

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
}