Import Question JSON

Current Question (ID: 16980)

Question:

$\text{A magnetic rod is inside a coil of wire which is connected to an ammeter. If the rod is stationary, which of the following statements is true?}$

Options:

1. $\text{The rod induces a small current.}$
2. $\text{The rod loses its magnetic field.}$
3. $\text{There is no induced current.}$
4. $\text{None of these.}$

Solution:

$\text{Hint: Since the magnetic rod is stationary, there is no change in magnetic flux through the coil, so no induced current is generated.}$ $\text{Explanation: Let's analyze the situation step by step:}$ $\text{A magnetic rod is placed inside a coil of wire that is connected to an ammeter. The rod is stationary (not moving).}$ $\text{Faraday's Law of Induction: Faraday's Law states that an electromotive force (EMF) is induced in a coil when there is a change in magnetic flux through the coil. This change can occur due to the motion of the magnet or a change in the strength or direction of the magnetic field. The induced current depends on the rate of change of the magnetic flux.}$ $\text{Stationary Rod: Since the rod is stationary, there is no movement of the magnetic field within the coil. The magnetic field around the rod remains constant over time.}$ $\text{Constant Magnetic Flux: Because the rod is not moving, the magnetic flux through the coil also remains constant. According to Faraday's Law, no change in magnetic flux means no induced EMF.}$ $\text{Induced Current: For an induced current to appear in the coil (which would be registered on the ammeter), there must be a change in the magnetic flux. Since the rod is stationary and the magnetic field is not changing, no current will be induced in the coil.}$ $\text{Hence, option (3) is the correct answer.}$

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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
}