Import Question JSON

Current Question (ID: 20361)

Question:

$\text{A charged particle going around in a circle can be considered to be a current loop. A particle of mass } m \text{ carrying charge } q \text{ is moving in a plane with speed } v \text{ under the influence of a magnetic field } \vec{B}. \text{ The magnetic moment of this moving particle:}$

Options:

1. $\frac{mv^2 \vec{B}}{B^2}$
2. $\frac{mv^2 \vec{B}}{2\pi B^2}$
3. $\frac{mv^2}{2B^2}$
4. $\frac{mv^2 \vec{B}}{2B^2}$

Solution:

$\text{Hint: } M = IA$ $\text{Magnetic moment}$ $M = iA$ $M = \left(\frac{q}{T}\right) \times \pi r^2 = \frac{q \pi r^2}{\left(\frac{2\pi}{v}\right)} = \frac{qvr}{2}$ $M = \frac{qv}{2} \times \frac{vm}{qB}$ $M = \frac{mv^2}{2B}$ $\text{As we can see from the figure, direction of magnetic moment (M) is opposite to magnetic field}$ $\vec{M} = \frac{mv^2}{-2B} \vec{B} = -\frac{mv^2}{2B^2} \vec{B}$

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
}