Import Question JSON

Current Question (ID: 20428)

Question:

$\text{The electric current in a circular coil of 2 turns produces a magnetic induction } B_1 \text{ at its centre.}$ $\text{The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction } B_2 \text{ at its centre.}$ $\text{The ratio of } \frac{B_2}{B_1} \text{ is:}$

Options:

1. $\frac{5}{25}$
2. $\frac{5}{2}$
3. $\frac{4}{5}$
4. $\frac{25}{2}$

Solution:

$\text{The magnetic field at the center of a circular coil is given by } B = \frac{\mu_0 n I}{2R}.$ $\text{For the first coil with 2 turns: } B_1 = \frac{\mu_0 \times 2 \times I}{2R}.$ $\text{For the second coil with 5 turns: } B_2 = \frac{\mu_0 \times 5 \times I}{2R}.$ $\text{Thus, the ratio } \frac{B_2}{B_1} = \frac{5}{2}.$

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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
}