Import Question JSON

Current Question (ID: 20623)

Question:

$\text{Average energy density of an EM wave with electric field amplitude } E_0 \text{ and magnetic field amplitude } B_0 \text{ is equal to}$

Options:

1. $\frac{1}{2} \varepsilon_0 E_0^2$
2. $\frac{B_0^2}{\mu_0}$
3. $\varepsilon_0 E_0^2$
4. $\frac{1}{2} \mu_0 E_0^2$

Solution:

$\text{Hint: An electromagnetic wave has both electric and magnetic fields.}$ $\text{Total energy} = \frac{1}{4} \varepsilon_0 E_0^2 + \frac{1}{4} \frac{B^2}{\mu_0}$ $\text{and } \varepsilon_0 E_0^2 = \frac{B^2}{\mu_0}$ $\Rightarrow \text{ total energy} = \frac{1}{2} \varepsilon_0 E_0^2$

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
}