Import Question JSON

Current Question (ID: 16865)

Question:

$\text{Two identical bar magnets are kept as shown in the figure. The direction of the resultant magnetic field, indicated by the arrowhead at the point } P \text{ is:}$

Options:

1. $\rightarrow$
2. $\nearrow$
3. $\nwarrow$
4. $\searrow$

Solution:

$\text{Hint: The direction of the magnetic field due bar magnet at an axial point is always along the magnetic dipole.}$ $\text{Step: Find the direction of the resultant magnetic field.}$ $\text{The magnetic field due to a bar magnet at the axial position is given by;} \ B_{\text{axial}} = \frac{2MB}{r^3}$ $\text{The magnetic field due to a bar magnet at the equatorial position is given by;} \ B_{\text{equatorial}} = \frac{MB}{r^3}$ $\text{The net magnetic field due to both bar magnets at the point } P \text{ is given by;} \ B_{\text{net}} = \sqrt{\left(\frac{MB}{r^3}\right)^2 + \left(\frac{2MB}{r^3}\right)^2} = \sqrt{5} \frac{MB}{r^3}$ $\text{The direction of the magnetic field } B_{\text{net}} \text{ at the point } P \text{ is shown in the figure below;}$ $\text{Therefore, the direction of the resultant magnetic field at point } P \text{ is } \searrow. \text{ Hence, option (4) is the correct answer.}$

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
}