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Current Question (ID: 16570)

Question:
$\text{Two parallel metal plates having charges } +Q \text{ and } -Q, \text{ face each other at a certain distance between them. If the plates are now dipped in the kerosene oil tank, the electric field between the plates will:}$ $1. \text{ increase}$ $2. \text{ decrease}$ $3. \text{ remain the same}$ $4. \text{ become zero}$
Options:
  • 1. $\text{increase}$
  • 2. $\text{decrease}$
  • 3. $\text{remain the same}$
  • 4. $\text{become zero}$
Solution:
$\text{Hint: } E = \frac{\sigma}{\varepsilon_0}$ $\text{Explanation: We have two parallel metal plates with charges } +Q \text{ and } -Q. \text{ The electric field } (E) \text{ between two parallel plates is given by:}$ $\Rightarrow E = \frac{\sigma}{\varepsilon_0}$ $\text{where } \sigma \text{ is the surface charge density and } \varepsilon_0 \text{ is the permittivity of free space.}$ $\text{When the plates are dipped into a dielectric medium (in this case, kerosene oil), the electric field is modified. The new electric field } E' \text{ in the presence of a dielectric is given by:}$ $\Rightarrow E' = \frac{\sigma}{k\varepsilon_0}$ $\text{where } k \text{ is the dielectric constant of the medium.}$ $\text{The dielectric constant } k \text{ for kerosene oil is greater than 1 (typically around 2.2 to 2.5). This means that the electric field will be reduced when the dielectric is introduced.}$ $\text{Since } k > 1, \text{ it follows that:}$ $\Rightarrow E' < E$ $\text{This indicates that the electric field between the plates decreases when they are submerged in kerosene oil. Therefore, the electric field between the plates decreases when they are dipped into kerosene oil.}$ $\text{Hence, option (2) is the correct answer.}$

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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
}