Import Question JSON

Current Question (ID: 20418)

Question:

$\text{A long solenoid carrying a current produces a magnetic field } B \text{ along its axis.}$ $\text{If the current is doubled and the number of turns per cm is halved,}$ $\text{then the new value of the magnetic field will be equal to:}$

Options:

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

Solution:

$\text{The magnetic field inside a solenoid is given by } B = \mu_0 n I.$ $\text{If the current } I \text{ is doubled and the number of turns per cm } n \text{ is halved,}$ $\text{then the new magnetic field } B' = \mu_0 \left(\frac{n}{2}\right) (2I) = \mu_0 n I = B.$ $\text{Thus, the new value of the magnetic field is } B.$

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
}