Import Question JSON

Current Question (ID: 16833)

Question:

$\text{A current-carrying closed loop in the form of a right isosceles triangle } ABC \text{ is placed in a uniform magnetic field acting along with } AB. \text{ If the magnetic force on the arm } BC \text{ is } F, \text{ then what is the force on the arm } AC?$

Options:

1. $-F$
2. $F$
3. $2F$
4. $-2F$

Solution:

$\text{Hint: The net force on a closed loop is equal to zero.}$ $\text{Step 1: Find the net force on the loop.}$ $\text{Net force} = F_{AB} + F_{BC} + F_{CA}$ $\text{Step 2: Find the force on the arm } AC.$ $\text{Here, } F_{AB} = 0 \text{ because the magnetic field and current are in the same direction.}$ $\Rightarrow F_{BC} + F_{CA} = 0$ $\Rightarrow F_{CA} = -F_{BC} = -F$

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
}