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Current Question (ID: 20507)

Question:

$\text{Variation of the magnetic field through a coil of area } 4 \text{ m}^2 \text{ is shown in the figure. What is the emf induced in the coil (in mV)?}$

Options:

1. $8 \text{ mV}$
2. $16 \text{ mV}$
3. $4 \text{ mV}$
4. $2 \text{ mV}$

Solution:

$\text{Hint: } \varepsilon_{\text{induced}} = A \left( \frac{dB}{dt} \right)$ $\text{Step 1: Find the slope of the curve.}$ $\text{From the given figure, the slope of the curve is given by:}$ $\frac{dB}{dt} = 2 \text{ mT/s}$ $\text{Step 2: Find the emf induced in the coil.}$ $\text{The magnetic flux through the coil is given by } \phi = BA$ $\text{The EMF induced in the coil is given by:}$ $\varepsilon_{\text{induced}} = A \frac{dB}{dt}$ $\varepsilon_{\text{induced}} = 4 \times 2 \text{ mV} = 8 \text{ mV}$ $\text{Therefore, EMF induced in the coil is 8 mV.}$ $\text{Hence, option (1) is the correct answer.}$

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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
}