Import Question JSON

Current Question (ID: 16888)

Question:

$\text{A short magnetic dipole is placed at the origin with its dipole movement directed along the } +x\text{-axis.}$ $\text{If magnetic field induction at a point } P(r, 0) \text{ is } B \hat{i},$ $\text{the magnetic field induction at point } Q(0, 2r) \text{ will be:}$

Options:

1. $-\frac{B}{16} \hat{i}$
2. $-\frac{B}{8} \hat{j}$
3. $\frac{B}{16} \hat{j}$
4. $-\frac{B}{16} \hat{j}$

Solution:

$\text{(1) At axial point: } B = \frac{\mu_0}{4\pi} \frac{2M}{r^3}$ $\text{At equatorial point (at same distance):}$ $B' = \frac{\mu_0}{4\pi} \frac{M}{r^3} = \frac{1}{2} \frac{\mu_0}{4\pi} \frac{2M}{r^3} = \frac{1}{2} B$ $\text{At distance } 2r:$ $B' = \frac{\mu_0}{4\pi} \frac{M}{(2r)^3} = \frac{1}{8} \frac{\mu_0}{4\pi} \frac{M}{r^3} = \frac{1}{8} \frac{B}{2} = \frac{B}{16}$ $\text{The direction of magnetic field at the equatorial point will be opposite to the direction of magnetic field at the axial point.}$

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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
}