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Current Question (ID: 16911)

Question:

$\text{When a small ferromagnetic magnet is fully demagnetized, its coercivity is measured to be } 3 \times 10^3 \text{ Am}^{-1}. \text{ A solenoid of length } 10 \text{ cm, consisting of } 100 \text{ turns, is used to achieve this demagnetization. What should be the current flowing through the solenoid to completely demagnetize the magnet when placed inside it?}$

Options:

1. $6 \text{ A}$
2. $30 \text{ mA}$
3. $3 \text{ A}$
4. $1.5 \text{ A}$

Solution:

$\text{Hint: } B = \mu_0 n i$ $\text{Step: Find the current in a solenoid coil.}$ $\text{The magnetic field } B \text{ inside a solenoid is given by:}$ $B = \mu_0 n I$ $\text{Coercivity is the intensity of the magnetic field needed to demagnetize a material. The coercivity } H_c \text{ is related to the magnetic field inside the solenoid is given by:}$ $H_c = n I$ $\text{Where } H_c = 3 \times 10^3 \text{ A/m (the coercivity of the magnet).}$ $\text{The number of turns per unit length } n \text{ is:}$ $\Rightarrow n = \frac{N}{L} = \frac{100}{0.1} = 1000 \text{ turns/m}$ $\text{Now, using the equation for coercivity:}$ $H_c = n I$ $3 \times 10^3 = 1000 \times I$ $I = \frac{1000 \times 10^3}{3} = 3 \text{ A}$ $\text{Hence, option (3) is the correct answer.}$

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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
}