Import Question JSON

Current Question (ID: 16901)

Question:

$\text{Select the correct option based on the statements:}$ $\text{Statement I: The magnetic field of a circular loop at very far away point on the axial line varies with distance as like that of a magnetic dipole.}$ $\text{Statement II: The magnetic field due to magnetic dipole varies inversely with the square of the distance from the centre on the axial line.}$

Options:

1. $\text{Statement I is correct and Statement II is incorrect.}$
2. $\text{Statement I is incorrect and Statement II is correct.}$
3. $\text{Both Statement I and Statement II are correct.}$
4. $\text{Both Statement I and Statement II are incorrect.}$

Solution:

$\text{Hint: } B = \frac{2\mu_0 M}{4\pi r^3}$ $\text{Explanation: The magnetic field of a circular loop at a very far away point on the axial line behaves like that of a magnetic dipole. This statement is correct because, at large distances, the magnetic field of a circular current loop can indeed be approximated as that of a magnetic dipole.}$ $\text{The magnetic field due to a magnetic dipole varies inversely with the square of the distance from the center on the axial line. This statement is incorrect.}$ $\text{The magnetic field of a dipole decreases with the cube of the distance i.e., } (\propto \frac{1}{r^3}) \text{ along the axial line, not inversely with the square (which is the behavior of a point charge).}$ $\text{Hence, option (1) is the correct answer.}$

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
}