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Current Question (ID: 20614)

Question:

$\text{An electron is constrained to move along the } y\text{-axis with a speed of } 0.1\ c \ (c \text{ is the speed of light) in the presence of an electromagnetic wave, whose electric field is }$ $\vec{E} = 30 \hat{j} \sin(1.5 \times 10^7 t - 5 \times 10^{-2} x) \ \text{V/m. The maximum magnetic force experienced by the electron will be: (given }$ $c = 3 \times 10^8 \ \text{ms}^{-1} \text{ and electron charge } = 1.6 \times 10^{-19} \ \text{C})$

Options:

1. $1.6 \times 10^{-19} \ \text{N}$
2. $4.8 \times 10^{-19} \ \text{N}$
3. $3.2 \times 10^{-18} \ \text{N}$
4. $2.4 \times 10^{18} \ \text{N}$

Solution:

$\text{Hint: } \vec{F} = q(\vec{v} \times \vec{B})$ $\Rightarrow \vec{E} = \vec{E} = 30 \hat{j} \sin \left(1.5 \times 10^7 t - 5 \times 10^{-2} x \right)$ $\Rightarrow B = E/V = \frac{30}{1.5 \times 10^7} \times 5 \times 10^{-2}$ $= 10^{-7} \ \text{Tesla}$ $\Rightarrow F_{\text{mag}} = q \left(\vec{V} \times \vec{B} \right) = |qVB|$ $= 1.6 \times 10^{-19} \times 0.1 \times 3 \times 10^8 \times 10^{-7}$ $= 4.8 \times 10^{-19} \ \text{N}$

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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
}