Import Question JSON

Current Question (ID: 16912)

Question:

$\text{The relationship between permeability } \mu \text{ and the magnetising field } H \text{ for a sample of iron is given by: } \mu = \left( \frac{0.5}{H} + 8 \times 10^{-4} \right) \text{ henry per metre, where } H \text{ is measured in A/m. What value of } H \text{ is required to produce a magnetic induction of } 1.0 \text{ Wb/m}^2?$

Options:

1. $500 \text{ A/m}$
2. $0.625 \text{ A/m}$
3. $625 \text{ A/m}$
4. $5.25 \text{ A/m}$

Solution:

$\text{Hint: } B = \mu H$ $\text{Step: Find the value of } H.$ $\text{Given: } \mu = \left( \frac{0.5}{H} + 8 \times 10^{-4} \right) \text{ henry per metre, } B = 1 \text{ T}$ $\text{The magnetic field due to the sample of iron is given by; } B = \mu H$ $\Rightarrow 1 = \left( \frac{0.5}{H} + 8 \times 10^{-4} \right) H = 0.5 + 8 \times 10^{-4} H$ $\Rightarrow H = \frac{0.5}{8 \times 10^{-4}} = \frac{1}{16} \times 10^4 \text{ A/m}$ $\Rightarrow H = 0.0625 \times 10^4 = 625 \text{ A/m}$ $\text{Hence, option (3) is the correct answer.}$

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
}