Import Question JSON

Current Question (ID: 20608)

Question:

$\text{A red LED emits light at } 0.1 \text{ watt uniformly around it. The amplitude of the electric field of the light at a distance of } 1 \text{ m from the diode is:}$

Options:

1. $1.73 \text{ V/m}$
2. $2.45 \text{ V/m}$
3. $5.48 \text{ V/m}$
4. $7.75 \text{ V/m}$

Solution:

$\text{Hint: } I = \frac{P}{A} = \frac{1}{2} \varepsilon_0 E_0^2 c$ $I = \frac{P}{4 \pi r^2} = \frac{1}{2} \varepsilon_0 E_0^2 c$ $E_0 = \sqrt{\frac{2P}{4 \pi \varepsilon_0 r^2 c}}$ $= \sqrt{\frac{2 \times 0.1 \times 9 \times 10^9}{1^2 \times 3 \times 10^8}}$ $= \sqrt{6}$ $= 2.45 \text{ V/m}$

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
}