Import Question JSON

Current Question (ID: 16813)

Question:

$\text{What will happen if two thin, long parallel wires separated by a distance } d \text{ carry current } i \text{ in the same direction?}$

Options:

1. $\text{attract each other with a force per unit length of } \frac{\mu_0 i^2}{2 \pi d^2}.$
2. $\text{repel each other with a force per unit length of } \frac{\mu_0 i^2}{2 \pi d^2}.$
3. $\text{attract each other with a force per unit length of } \frac{\mu_0 i^2}{2 \pi d}.$
4. $\text{repel each other with a force per unit length of } \frac{\mu_0 i^2}{2 \pi d}.$

Solution:

$\text{Hint: Force on a current-carrying wire=} i \left( \vec{l} \times \vec{B} \right)$ $B = \frac{\mu_0 i}{2 \pi d}$ $\vec{F} = i \left( \vec{l} \times \vec{B} \right)$ $F = i l \left( \frac{\mu_0 i}{2 \pi d} \right)$ $\frac{F}{l} = \frac{\mu_0 i^2}{2 \pi d}$

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
}