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Current Question (ID: 17400)

Question:

$\text{The figure shows a parallel plate capacitor being charged by a battery. If } X \text{ and } Y \text{ are two closed curves then during charging, } \oint \vec{B} \cdot d\vec{l} \text{ is zero along the curve:}$

Options:

1. $X \text{ only}$
2. $Y \text{ only}$
3. $\text{Both } X \& Y$
4. $\text{Neither } X \text{ nor } Y$

Solution:

$\text{Hint: Whenever the capacitor is getting charged then there will be a conduction current as well as a displacement current.}$ $\text{Step 1: Find the magnetic field for the loop } Y.$ $\text{In this loop, there is only a conduction current.}$ $\text{The magnetic field for the loop } Y \text{ is given by:}$ $\Rightarrow \oint \vec{B} \cdot d\vec{l} = \mu_0 [i_c + i_d] = \mu_0 i_c \neq 0$ $\text{Step 2: Find the magnetic field for the loop } X.$ $\text{In this loop, there is only a displacement current.}$ $\text{The magnetic field for the loop } X \text{ is given by:}$ $\text{So, } \oint \vec{B} \cdot d\vec{l} = \mu_0 [i_c + i_d] = \mu_0 i_d \neq 0.$ $\text{Hence, option (4) is the correct answer.}$

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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
}