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Current Question (ID: 20612)

Question:

$\text{The magnetic field of a plane electromagnetic wave is given by:}$ $\vec{B} = 3 \times 10^{-8} \sin[200\pi(y + ct)] \hat{i} \ \text{T}$ $\text{Where} \ c = 3 \times 10^8 \ \text{m/s is the speed of light. The corresponding electric field is:}$

Options:

1. $\vec{E} = -10^{-6} \sin[200\pi(y + ct)] \hat{k} \ \text{V/m}$
2. $\vec{E} = 3 \times 10^{-8} \sin[200\pi(y + ct)] \hat{k} \ \text{V/m}$
3. $\vec{E} = -9 \sin[200\pi(y + ct)] \hat{k} \ \text{V/m}$
4. $\vec{E} = 9 \sin[200\pi(y + ct)] \hat{k} \ \text{V/m}$

Solution:

$\text{Hint:} \ E_0 = cB_0$ $\vec{B} = 3 \times 10^{-8} \sin \left[ 200 \pi \left( y + ct \right) \right]$ $E_0 = cB_0 = 3 \times 10^8 \times 3 \times 10^{-8} = 9 \ \text{V/m}$ $\text{and direction of wave propagation is given as}$ $\left( \vec{E} \times \vec{B} \right) \parallel \vec{C}$ $\hat{B} = \hat{i} \ \text{and} \ \hat{C} = -\hat{j}$ $\text{so} \ \hat{E} = -\hat{k}$ $\therefore \vec{E} = E_0 \sin \left[ 200\pi \left( y + ct \right) \right] \left( -\hat{k} \right)$

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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
}