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Current Question (ID: 17420)

Question:

$\text{The magnetic field in a plane electromagnetic wave is given by}$ $B_z = 2 \times 10^{-7} \sin(0.5 \times 10^3 x - 1.5 \times 10^{11} t) \text{ T.}$ $\text{The expression for the electric field will be:}$

Options:

1. $E_z = 30 \sqrt{2} \sin(0.5 \times 10^3 x - 1.5 \times 10^{11} t) \text{ V/m}$
2. $E_z = 60 \sin(0.5 \times 10^3 x - 1.5 \times 10^{11} t) \text{ V/m}$
3. $E_y = 30 \sqrt{2} \sin(0.5 \times 10^{11} x - 1.5 \times 10^3 t) \text{ V/m}$
4. $E_y = 60 \sin(0.5 \times 10^3 x - 1.5 \times 10^{11} t) \text{ V/m}$

Solution:

$\vec{B} \text{ is along +z direction.}$ $\text{EM wave travels along the -x direction.}$ $\text{The direction of } \vec{E} \times \vec{B} \text{ gives the direction of the wave.}$ $\therefore \vec{E} \text{ is along the y-direction.}$ $\text{The amplitude of the electric field,}$ $E_0 = B_0 c$ $= 2 \times 10^{-7} \times 3 \times 10^8$ $= 60 \text{ V/m}$ $\therefore \text{Electric field, } E_y = 60 \sin(0.5 \times 10^3 x - 1.5 \times 10^{11} t)$

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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
}