Import Question JSON

Current Question (ID: 16778)

Question:

$\text{The magnetic force acting on a charged particle of charge } -2 \, \mu\text{C} \text{ in a magnetic field of } 2 \, \text{T acting in the } y\text{-direction, when the particle velocity is } (2\hat{i} + 3\hat{j}) \times 10^6 \, \text{ms}^{-1} \text{ is:}$

Options:

1. $8 \, \text{N in } -z\text{-direction.}$
2. $4 \, \text{N in the } z\text{-direction.}$
3. $8 \, \text{N in the } y\text{-direction.}$
4. $8 \, \text{N in the } z\text{-direction.}$

Solution:

$\text{Hint: The magnetic force depends on the direction of the particle's velocity w.r.t the magnetic field.}$ $\text{Step 1: Find the formula of magnetic force.}$ $\text{Lorentz's force is given by:}$ $\vec{F} = q \left( \vec{v} \times \vec{B} \right)$ $\text{Step 2: Put the given values.}$ $\vec{F} = -2 \times 10^{-6} \times \left[ (2\hat{i} + 3\hat{j}) \times 2\hat{j} \right] \times 10^6$ $\vec{F} = -8\hat{k}$

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
}