Import Question JSON

Current Question (ID: 16765)

Question:

$\text{An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of } i \text{ amperes and the radius of the circular loop is } r \text{ metres. What will be the magnetic induction at its centre?}$

Options:

1. $\frac{\mu_0}{4\pi} \frac{2i}{r} (\pi + 1)$
2. $\frac{\mu_0}{4\pi} \frac{2i}{r} (\pi - 1)$
3. $\text{zero}$
4. $\text{Infinite}$

Solution:

$\text{The given shape is equivalent to the following diagram}$ $\text{The field at } O \text{ due to straight part of conductor is } B_1 = \frac{\mu_0}{4\pi} \frac{2i}{r} \odot.$ $\text{The field at } O \text{ due to circular coil is } B_2 = \frac{\mu_0}{4\pi} \frac{2\pi i}{r} \otimes.$ $\text{Both fields will act in the opposite direction, hence the total field at } O.$ $\text{i.e. } B = B_2 - B_1 = \left( \frac{\mu_0}{4\pi} \right) \times (\pi - 1) \frac{2i}{r} = \frac{\mu_0}{4\pi} \frac{2i}{r} (\pi - 1)$

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
}