Import Question JSON

Current Question (ID: 16817)

Question:

$\text{An arrangement of three parallel straight wires placed perpendicular to the plane of paper carrying the same current in the same direction is shown in the figure. The magnitude of force per unit length on the middle wire } B \text{ is given by:}$

Options:

1. $\frac{\mu_0 i^2}{2 \pi d}$
2. $\frac{2 \mu_0 i^2}{\pi d}$
3. $\frac{\pi d}{\sqrt{2} \mu_0 i^2}$
4. $\frac{\mu_0 i^2}{\sqrt{2 \pi d}}$

Solution:

$\text{Hint: } F_{\text{net}} = \sqrt{F_1^2 + F_2^2}$ $\text{Step: Find the magnitude of force per unit length on the middle wire } B$ $\text{As the force on the wire } B \text{ is due to } A \text{ and } C \text{ attractive, so we have the following conditions:}$ $F = \frac{\mu_0 I^2}{2 \pi d}$ $\text{The resultant force on } B \text{ is given by:}$ $F_{\text{net}} = \sqrt{F_1^2 + F_2^2}$ $F_{\text{net}} = \sqrt{2} F$ $F_{\text{net}} = \sqrt{2} \times \frac{\mu_0 I^2}{2 \pi d} = \frac{\mu_0 I^2}{\sqrt{2 \pi d}}$ $\text{Hence, option (4) is the correct answer.}$

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
}