Import Question JSON

Current Question (ID: 16802)

Question:

$\text{Magnetic field at the outer surface of long hollow cylindrical shells of radius } R$ $\text{and carrying current } I \text{ is } B. \text{ What is the magnetic field at a distance of } \frac{3R}{2}$ $\text{ from the axis of the cylindrical shell?}$

Options:

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

Solution:

$\text{Hint: Apply Ampere's circuital law.}$ $\text{Step 1: Find } B_s.$ $B_s = B = \frac{\mu_0}{2\pi} \frac{I}{R}.$ $\text{Step 2: Find } B_{\frac{3R}{2}}.$ $B_{\frac{3R}{2}} = \frac{\mu_0}{2\pi} \frac{2I}{3R} = \frac{2}{3} \frac{\mu_0}{2\pi} \frac{I}{R} = \frac{2}{3} B$

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
}