Import Question JSON

Current Question (ID: 16783)

Question:

$\text{A particle with charge } q, \text{ moving with a momentum } p, \text{ enters a uniform magnetic field normally.}$ $\text{The magnetic field has magnitude } B \text{ and is confined to a region of width } d, \text{ where } d < \frac{p}{Bq}. \text{ The particle is deflected by an angle } \theta \text{ in crossing the field, then:}$

Options:

1. $\sin \theta = \frac{Bqd}{p}$
2. $\sin \theta = \frac{p}{Bqd}$
3. $\sin \theta = \frac{Bp}{qd}$
4. $\sin \theta = \frac{pd}{Bq}$

Solution:

$\text{From figure it is clear that } \sin \theta = \frac{d}{r} \text{ also } r = \frac{p}{qB}$ $\therefore \sin \theta = \frac{Bqd}{p}$

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
}