Import Question JSON

Current Question (ID: 20439)

Question:

$\text{Coil A of radius 10 cm has } N_A \text{ number of turns and } I_A \text{ current is flowing through it. Coil B of radius 20 cm has } N_B \text{ number of turns and } I_B \text{ current is flowing through it. If the magnetic dipole moment of both the coils is the same then:}$

Options:

1. $I_A N_A = 4 I_B N_B$
2. $4 I_A N_A = I_B N_B$
3. $I_A N_A = 2 I_B N_B$
4. $2 I_A N_A = I_B N_B$

Solution:

$\text{Magnetic dipole moment, } \mu = N i A = N i \pi R^2$ $\frac{\mu_A}{\mu_B} = \frac{N_A i_A R_A^2}{N_B i_B R_B^2} = 1$ $\text{So, } \frac{N_A i_A 10^2}{N_B i_B 20^2} = 1$ $N_A i_A = 4 N_B i_B$

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
}