Import Question JSON

Current Question (ID: 16770)

Question:

$\text{A cell is connected between the points } A \text{ and } C \text{ of a circular conductor } ABCD \text{ of centre } O \text{ with an angle of } AOC = 60^\circ.$ $\text{If } B_1 \text{ and } B_2 \text{ are the magnitudes of the magnetic fields at } O \text{ due to the currents in } ABC \text{ and } ADC \text{ respectively, the ratio } B_1 : B_2 \text{ will be:}$

Options:

1. $0.2$
2. $6$
3. $1$
4. $5$

Solution:

$\text{B} = \frac{\mu_0}{4\pi} \frac{\theta_i}{r} \Rightarrow \text{B} \propto \theta_i$ $\left( \text{but } \frac{i_1}{i_2} = \frac{l_1}{l_2} = \frac{\theta_2}{\theta_1} \right)$ $\Rightarrow \frac{B_1}{B_2} = \frac{\theta_1}{\theta_2} \cdot \frac{i_1}{i_2}$ $\text{So, } \frac{B_1}{B_2} = \frac{\theta_1}{\theta_2} \times \frac{\theta_2}{\theta_1}$ $\Rightarrow B_1 = B_2$

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
}