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Current Question (ID: 16473)

Question:
$\text{Given below are two statements:}$ $\text{Statement I:}$ $\text{Gauss's law for electric fields is a consequence of the conservation of energy.}$ $\text{Statement II:}$ $\text{Coulomb's law for electric charges leads to a conservative electric field.}$
Options:
  • 1. $\text{Statement I is incorrect and Statement II is correct.}$
  • 2. $\text{Both Statement I and Statement II are correct.}$
  • 3. $\text{Both Statement I and Statement II are incorrect.}$
  • 4. $\text{Statement I is correct and Statement II is incorrect.}$
Solution:
$\text{Hint: The electrostatic field is a conservative field.}$ $\text{Explanation: Gauss' law concerns the electric flux. It is in no way connected to the conservation of energy.}$ $\text{The electric flux through a closed surface to the charge enclosed.}$ $\text{Gauss's law is a direct consequence of Coulomb's law and is derived using the concept of field lines spreading radially from a charge.}$ $\text{It is a mathematical restatement of the inverse square law, which relates to charge distribution.}$ $\text{It has no direct connection with the conservation of energy.}$ $\text{Conservation of energy applies to the work done by the field, but Gauss's law arises from the symmetry of electric fields, not energy conservation.}$ $\text{The electric field produced by a charge is conservative because the work done by the field is path-independent.}$ $\text{This is a key property of conservative fields.}$ $\text{Coulomb's law directly implies a conservative electric field which means the electric field has no curl.}$ $\text{Every central force is a conservative force and the Coulomb force is also a conservative force.}$ $\text{Hence, option (1) is the correct answer.}$

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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
}