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Current Question (ID: 16818)

Question:

$\text{Three long, straight, and parallel wires carrying currents of } 30 \text{ A, } 10 \text{ A, and } 20 \text{ A}$ $\text{in } P, Q, \text{ and } R, \text{ respectively, are arranged as shown in the figure.}$ $\text{What is the force experienced by a } 10 \text{ cm length of wire } Q?$

Options:

1. $1.4 \times 10^{-4} \text{ N towards the right}$
2. $1.4 \times 10^{-4} \text{ N towards the left}$
3. $2.6 \times 10^{-4} \text{ N to the right}$
4. $2.6 \times 10^{-4} \text{ N to the left}$

Solution:

$\text{(a) Force on wire } Q \text{ due to wire } P \text{ is}$ $F_p = 10^{-7} \times \frac{2 \times 30 \times 10}{0.1} \times 0.1 = 6 \times 10^{-5} \text{ N (Towards left)}$ $\text{Force on wire } Q \text{ due to wire } R \text{ is}$ $F_R = 10^{-7} \times \frac{2 \times 20 \times 10}{0.02} \times 0.1 = 20 \times 10^{-5} \text{ N (Towards right)}$ $\text{Hence, } F_{\text{net}} = F_R - F_p = 14 \times 10^{-5} \text{ N} = 1.4 \times 10^{-4} \text{ N (Towards right)}$

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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
}