Import Question JSON

Current Question (ID: 20446)

Question:

$\text{The characteristics of two coils are given below:}$ $\begin{array}{|c|c|c|} \hline & \text{Coil-A} & \text{Coil-B} \\ \hline \text{Radius} & r_A = 10 \text{ cm} & r_A = 20 \text{ cm} \\ \text{Number of turns} & N_A & N_B \\ \text{Current} & I_A \text{ ampere} & I_B \text{ ampere} \\ \hline \end{array}$ $\text{If the magnetic moments of both Coil-A and Coil-B are equal, choose the correct relation:}$

Options:

1. $2N_AI_A = N_BI_B$
2. $N_AI_A = N_BI_B$
3. $N_AI_A = 4N_BI_B$
4. $N_AI_A = 2N_BI_B$

Solution:

$\text{Hint: } m = NIA$ $\text{Step: Find the correct relation between } N \text{ and } I.$ $\text{Given: The magnetic moments of both Coil-A and Coil-B are equal.}$ $\text{The magnetic moment of the coil is given by:}$ $m = NIA$ $\Rightarrow m_A = m_B$ $\Rightarrow N_AI_A\pi(10 \text{ cm})^2 = N_BI_B\pi(20 \text{ cm})^2$ $\Rightarrow N_AI_A = 4N_BI_B$ $\text{Hence, option (3) is the correct answer.}$

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
}