Import Question JSON

Current Question (ID: 20340)

Question:

$\text{The dipole moment of a circular loop carrying a current } I, \text{ is } m \text{ and the magnetic field at the centre of the loop is } B_1. \text{ When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is } B_2. \text{ The ratio } \frac{B_1}{B_2} \text{ is:}$

Options:

1. $2$
2. $\sqrt{3}$
3. $\sqrt{2}$
4. $\frac{1}{\sqrt{2}}$

Solution:

$\text{Hint: } B = \frac{\mu_0 I(N)}{2r}$ $\therefore B = \frac{\mu_0 I(N)}{2r}$ $\therefore M = NIA$ $= NI(\pi r^2)$ $r = \sqrt{\frac{M}{NI\pi}}$ $B = \frac{\mu_0 IN}{2} \sqrt{\frac{M}{NI\pi}}$ $\Rightarrow B \propto \frac{1}{\sqrt{M}}$ $\Rightarrow \frac{B_1}{B_2} = \sqrt{2}$

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
}