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Current Question (ID: 16815)

Question:

$\text{A long wire } A \text{ carries a current of } 10 \text{ A. Another long wire } B, \text{ which is parallel to } A \text{ and separated by } 0.1 \text{ m from } A, \text{ carries a current of } 5 \text{ A, in the opposite direction to that in } A. \text{ What is the magnitude and nature of the force experienced per unit length of } B?$ $\left( \mu_0 = 4\pi \times 10^{-7} \text{ weber/(amp-m)} \right)$

Options:

1. $\text{Repulsive force of } 10^{-4} \text{ N/m}$
2. $\text{Attractive force of } 10^{-4} \text{ N/m}$
3. $\text{Repulsive force of } 2\pi \times 10^{-5} \text{ N/m}$
4. $\text{Attractive force of } 2\pi \times 10^{-5} \text{ N/m}$

Solution:

$(a) \quad F = \frac{\mu_0}{4\pi} \frac{2i_1i_2}{a} = 10^{-7} \times \frac{2 \times 10 \times 5}{0.1} = 10^{-4} \text{ N (Repulsive)}$

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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
}