Import Question JSON

Current Question (ID: 20067)

Question:

$\text{A wire, of length } (L = 20 \text{ cm}), \text{ is bent into a semicircular arc. If the two equal halves, of the area, were each to be uniformly charged with charges } \pm Q, \ |Q| = 10^3 \varepsilon_0 \ C, \text{ where } \varepsilon_0 \text{ is the permittivity (in S.I units) of free space} \text{ the net electric field at the centre } O \text{ of the semicircular area would be:}$

Options:

1. $(50 \times 10^3 \ \text{N/C}) \ \hat{j}$
2. $(50 \times 10^3 \ \text{N/C}) \ \hat{i}$
3. $(25 \times 10^3 \ \text{N/C}) \ \hat{j}$
4. $(25 \times 10^3 \ \text{N/C}) \ \hat{i}$

Solution:

$\text{Hint: } E = \frac{2k\lambda}{R}$

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
}