Import Question JSON

Current Question (ID: 20449)

Question:

$\text{A proton having velocity } \vec{v}_0 \text{ passes through a region having an electric field } E \text{ and a magnetic field } B. \text{ If the velocity of a proton does not change, then which of the following may be true?}$ $\text{a. } E = 0, B = 0$ $\text{b. } E = 0, B \neq 0$ $\text{c. } E \neq 0, B = 0$ $\text{d. } E \neq 0, B \neq 0$

Options:

1. $(\text{a}), (\text{b}), (\text{c}), (\text{d})$
2. $(\text{a})$
3. $(\text{a}), (\text{b}), (\text{d})$
4. $(\text{a}), (\text{b})$

Solution:

$\text{Hint: } \vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$ $\vec{F}_E = q\vec{E}$ $\vec{F}_B = q(\vec{v} \times \vec{B})$ $\text{Case b is correct when } \vec{V} \parallel \vec{B}$ $\text{Case d is correct when } \vec{E} \perp \vec{B} \perp \vec{V} \text{ and } V = \frac{E}{B}$

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
}