Import Question JSON

Current Question (ID: 16794)

Question:

$\text{If charge } -Q \text{ is moving vertically upwards, then what will be the force on the charged particle if it enters a magnetic field that is pointed towards the south?}$ $1. \text{ North}$ $2. \text{ South}$ $3. \text{ East}$ $4. \text{ West}$

Options:

1. $\text{North}$
2. $\text{South}$
3. $\text{East}$
4. $\text{West}$

Solution:

$\text{Hint: } \vec{F} = q \left( \vec{v} \times \vec{B} \right)$ $\text{Step 1: Draw the diagram.}$ $\text{The magnetic field is along the South.}$ $\text{Step 2: Use the formula for Lorentz force.}$ $\vec{F} = -q \left( \vec{v} \times \vec{B} \right)$ $\text{The direction of } \left( \vec{v} \times \vec{B} \right) \text{ is along the East. Hence the magnetic force on the particle is along the West.}$

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
}