Import Question JSON

Current Question (ID: 20356)

Question:

$\text{A wire } A, \text{ bent in the shape of an arc of a circle, carrying a current of } 2 \text{ A and having radius } 2 \text{ cm and another wire } B, \text{ also bent in the shape of arc of a circle, carrying a current of } 3 \text{ A and having radius of } 4 \text{ cm, are placed as shown in the figure. The ratio of the magnetic fields due to the wires } A \text{ and } B \text{ at the common centre } O \text{ is:}$

Options:

1. $6 : 5$
2. $6 : 4$
3. $2 : 5$
4. $4 : 6$

Solution:

$\text{Hint: } B = \frac{\mu_0 I \theta}{4 \pi R}$ $\text{Given } i_A = 2, \ r_A = 2 \text{ cm}, \ \theta_A = 2\pi - \frac{\pi}{2} = \frac{3\pi}{2}$ $i_B = 3, \ r_B = 4 \text{ cm}, \ \theta_B = 2\pi - \frac{\pi}{3} = \frac{5\pi}{3}$ $\frac{B_A}{B_B} = \frac{I_A}{I_B} \times \frac{\theta_A r_B}{\theta_B r_A} = \frac{6}{5}$

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
}