Import Question JSON

Current Question (ID: 20105)

Question:

$\text{A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge } Q \text{ (having a charge equal to the sum of the charges on the } 4 \, \mu\text{F and } 9 \, \mu\text{F capacitors), at a point distant } 30 \, \text{m from it, would equal:}$

Options:

1. $240 \, \text{N/C}$
2. $360 \, \text{N/C}$
3. $420 \, \text{N/C}$
4. $480 \, \text{N/C}$

Solution:

$\text{Hint: } q = C_{\text{eq}} V$ $q = C_{\text{eq}} V = \left( \frac{4 \times 12}{4 + 12} \right) \times 8 = 24 \, \mu\text{C}$ $q_1 = \frac{9}{9 + 3} \times 24 \, \mu\text{C} = 18 \, \mu\text{C}$ $\therefore Q = q + q_1 = 24 + 18 = 42 \, \mu\text{C}$ $E = \frac{KQ}{r^2} = \frac{9 \times 10^9 \times 42 \times 10^{-6}}{(30)^2} = 420 \, \text{N/C}$

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
}