Import Question JSON

Current Question (ID: 20677)

Question:

$\text{The magnetic field in a plane electromagnetic wave is}$ $B_y = (3.5 \times 10^{-7}) \sin(1.5 \times 10^3 x + 0.5 \times 10^{11} t) \text{ T. The corresponding electric field will be:}$

Options:

1. $E_z = 105 \sin(1.5 \times 10^3 x + 0.5 \times 10^{11} t) \text{ Vm}^{-1}$
2. $E_y = 1.17 \sin(1.5 \times 10^3 x + 0.5 \times 10^{11} t) \text{ Vm}^{-1}$
3. $E_z = 1.17 \sin(1.5 \times 10^3 x + 0.5 \times 10^{11} t) \text{ Vm}^{-1}$
4. $E_y = 10.5 \sin(1.5 \times 10^3 x + 0.5 \times 10^{11} t) \text{ Vm}^{-1}$

Solution:

$\text{The electric field is related to the magnetic field by the equation:}$ $E = cB$ $\text{where } c = 3 \times 10^8 \text{ m/s is the speed of light.}$ $\text{Given } B_y = 3.5 \times 10^{-7} \text{ T,}$ $E_z = c \times B_y = 3 \times 10^8 \times 3.5 \times 10^{-7} = 105 \text{ Vm}^{-1}$ $\text{Thus, the correct option is 1.}$

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
}