Import Question JSON

Current Question (ID: 17438)

Question:

$\text{A lamp emits monochromatic green light uniformly in all directions. The lamp is } 3\% \text{ efficient in converting electrical power to electromagnetic waves and consumes } 100 \text{ W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of } 5 \text{ m from the lamp will be:}$

Options:

1. $1.34 \text{ V/m}$
2. $2.68 \text{ V/m}$
3. $4.02 \text{ V/m}$
4. $5.36 \text{ V/m}$

Solution:

$\text{Power of Em waves } = 3\% \text{ of } 100 \text{ W } = 3 \text{ W}$ $\text{Intensity}=\frac{P}{A}=\frac{3}{4\pi(5)^2}=0.0096 \frac{W}{m^2}$ $\text{Then, } I = \frac{1}{2} \varepsilon_0 c E_0^2$ $\Rightarrow E_0 = \sqrt{\frac{2I}{\varepsilon_0 c}} = 2.68 \text{ V/m}$

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
}