Import Question JSON

Current Question (ID: 20634)

Question:

$\text{The magnetic field of a plane electromagnetic wave is given by:}$ $\mathbf{B} = B_0 \hat{i} [\cos(kz - \omega t)] + B_1 \hat{j} [\cos(kz - \omega t)]$ $\text{where}$ $B_0 = 3 \times 10^{-5} \text{ T and } B_1 = 2 \times 10^{-6} \text{ T.}$ $\text{The rms value of the force experienced by a stationary charge } Q = 10^{-4} \text{ C at } z = 0 \text{ is closest to:}$

Options:

1. $0.6 \text{ N}$
2. $3 \times 10^{-2} \text{ N}$
3. $0.9 \text{ N}$
4. $0.1 \text{ N}$

Solution:

$\text{Hint: } \mathbf{F}_{\text{net}} = q \mathbf{E}_{\text{net}}$ $\text{Maximum Electric Field = BC}$ $F_{\text{net}} = q \mathbf{E}_{\text{net}}$ $= qC(-3 \times 10^{-5} \hat{j} - 2 \times 10^{-6} \hat{i})$ $= 10^{-4} \times 3 \times 10^8$ $= 9 \text{ N}$ $F_{\text{rms}} = \frac{F_0}{\sqrt{2}} = 0.6 \text{ N}$

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
}