Import Question JSON

Current Question (ID: 16882)

Question:

$\text{The magnetic field at a point } x \text{ on the axis of a small bar magnet is equal to the field at a point } y \text{ on the equator of the same magnet.}$ $\text{The ratio of the distances of } x \text{ and } y \text{ from the centre of the magnet is:}$

Options:

1. $2^{-3}$
2. $2^{-\frac{1}{3}}$
3. $2^3$
4. $2^{\frac{1}{3}}$

Solution:

$\text{For a bar magnet, the magnetic field on the axis is given by } B_\text{axis} = \frac{\mu_0}{4\pi} \cdot \frac{2M}{x^3}.$ $\text{The magnetic field on the equator is given by } B_\text{equator} = \frac{\mu_0}{4\pi} \cdot \frac{M}{y^3}.$ $\text{Given } B_\text{axis} = B_\text{equator}, \text{ we have } \frac{2M}{x^3} = \frac{M}{y^3}.$ $\text{This simplifies to } \frac{x^3}{y^3} = 2, \text{ or } \left(\frac{x}{y}\right)^3 = 2.$ $\text{Thus, } \frac{x}{y} = 2^{\frac{1}{3}}.$

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
}