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Current Question (ID: 20389)

Question:

$\text{A wire carrying current } I \text{ is tied between points } P \text{ and } Q \text{ and is in the shape of a circular arch of radius } R \text{ due to a uniform magnetic field } B \text{ (perpendicular to the plane of the paper, shown by cross marked) in the vicinity of the wire. If the wire subtends an angle } 2\theta_0 \text{ at the centre of the circle (of which it forms an arch) then the tension in the wire is:}$

Options:

1. $\frac{IBR}{2 \sin \theta_0}$
2. $IBR \theta_0$
3. $\frac{IBR}{\sin \theta_0}$
4. $IBR$

Solution:

$\text{Use symmetry + horizontal components of magnetic force}$

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
}