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Current Question (ID: 20062)

Question:

$\text{A dipole, with a charge of magnitude } 0.01 \text{ C and a separation distance of } 0.4 \text{ mm, is positioned within an electric field that has a strength of } 10 \text{ dyne/C. The maximum torque exerted on the dipole in this field is:}$

Options:

1. $4 \times 10^{-9} \text{ N-m}$
2. $2 \times 10^{-10} \text{ N-m}$
3. $4 \times 10^{-10} \text{ N-m}$
4. $2 \times 10^{-9} \text{ N-m}$

Solution:

$\text{Hint: } |\tau| = |\vec{P} \times \vec{E}|$ $\text{Step: Find the maximum torque exerted on the dipole.}$ $\text{The magnitude of the dipole is given by:}$ $p = 0.01 \times 0.4 \times 10^{-3} = 4 \times 10^{-6} \text{ m}$ $\text{The magnitude of the electric field is given by:}$ $E = 10 \times 10^{-5} \text{ N} \quad [1 \text{ dyne} = 10^{-5} \text{ N}]$ $\text{The torque exerted on the dipole is given by:}$ $\tau = \vec{p} \times \vec{E}$ $\Rightarrow |\tau|_{\text{max}} = |\vec{p}||\vec{E}|$ $\Rightarrow |\tau| = 4 \times 10^{-6} \times 10 \times 10^{-5} = 4 \times 10^{-10} \text{ N-m}$ $\text{Therefore, the maximum torque exerted on the dipole is } 4 \times 10^{-10} \text{ N-m.}$ $\text{Hence, option (3) is the correct answer.}$

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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
}