Import Question JSON

Current Question (ID: 20636)

Question:

$\text{The electric field of a plane electromagnetic wave is given by:}$ $\vec{E} = E_0 \hat{i} \cos(kz) \cos(\omega t)$ $\text{The corresponding magnetic field } \vec{B} \text{ is then given by:}$

Options:

1. $\vec{B} = \frac{E_0}{c} \hat{k} \sin(kz) \cos(\omega t)$
2. $\vec{B} = \frac{E_0}{c} \hat{i} \sin(kz) \cos(\omega t)$
3. $\vec{B} = \frac{E_0}{c} \hat{j} \sin(kz) \cos(\omega t)$
4. $\vec{B} = \frac{E_0}{c} \hat{j} \cos(kz) \cos(\omega t)$

Solution:

$\text{Hint: } \frac{E_0}{B_0} = c$ $\vec{E} = E_0 \cos kz \cos \omega t \hat{i}$ $\text{vibration of } B \text{ = perpendicular to } \vec{E} \text{ and propagation of electromagnetic wave is in } z \text{ direction.}$ $\text{Hence the direction of vibration of } \vec{B} \text{ should be along } \hat{j}$ $\frac{E_0}{B_0} = C$ $\vec{B} = \frac{E_0}{C} \cos \omega t \cos kz \hat{j}$

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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
}