Import Question JSON

Current Question (ID: 16777)

Question:

$\text{A beam of electrons passes un-deflected through mutually perpendicular electric and magnetic fields. Where do the electrons move if the electric field is switched off and the same magnetic field is maintained?}$

Options:

1. $\text{in an elliptical orbit.}$
2. $\text{in a circular orbit.}$
3. $\text{along a parabolic path.}$
4. $\text{along a straight line.}$

Solution:

$\text{Hint: Initially the electric force balances the magnetic force.}$ $\text{Step 1: Find the direction of motion of the electrons.}$ $\text{The particle is moving perpendicular to both of them with } F_e = F_m. \text{ In this situation, } \vec{E} \neq 0 \text{ and } \vec{B} \neq 0.$ $\text{Step 2: Find the final force on the electrons.}$ $\text{But if the electric field becomes zero, then only force due to the magnetic field exists. Under this force, the charge moves along a circle.}$

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
}