Import Question JSON

Current Question (ID: 20352)

Question:

$\text{A wire carrying current } I \text{ is bent in the shape } ABCDEFA \text{ as shown, where rectangle } ABCDA \text{ and } ADEF \text{A are perpendicular to each other. If the sides of the rectangles are of lengths } a \text{ and } b, \text{ then the magnitude and direction of magnetic moment of the loop } ABCDEFA \text{ is:}$

Options:

1. $\sqrt{2} abI \text{ along } \left[ \frac{\hat{j}}{\sqrt{2}} + \frac{\hat{k}}{\sqrt{2}} \right]$
2. $\sqrt{2} abI \text{ along } \left[ \frac{\hat{j}}{\sqrt{5}} + \frac{2\hat{k}}{\sqrt{5}} \right]$
3. $abI \text{ along } \left[ \frac{\hat{j}}{\sqrt{2}} + \frac{\hat{k}}{\sqrt{2}} \right]$
4. $abI \text{ along } \left[ \frac{\hat{j}}{\sqrt{5}} + \frac{2\hat{k}}{\sqrt{5}} \right]$

Solution:

$\text{Hint: } m = IA$ $M = NIA$ $N = I$ $\text{For } ABCD$ $\vec{M}_1 = abI \hat{K}$ $\text{For } DEFA$ $\vec{M}_2 = abI \hat{j}$ $\vec{M} = \vec{M}_1 + \vec{M}_2$ $= abI \left( \hat{k} + \hat{j} \right)$ $= abI \sqrt{2} \left( \frac{\hat{j}}{\sqrt{2}} + \frac{\hat{k}}{\sqrt{2}} \right)$

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
}