Import Question JSON

Current Question (ID: 16471)

Question:

$\text{Given below are two statements:}$ $\text{Statement I: Electrostatic field lines never form closed loops.}$ $\text{Statement II: Gauss's law is particularly useful for calculating the}$ $\text{electrostatic field in systems that lack symmetry.}$

Options:

1. $\text{Statement I is correct while Statement II is incorrect.}$
2. $\text{Statement II is correct while Statement I is incorrect.}$
3. $\text{Both Statement I and Statement II are correct.}$
4. $\text{Both Statement I and Statement II are incorrect.}$

Solution:

$\text{Hint: The electric force is conservative in nature.}$ $\text{Explanation: Electrostatic force is conservative in nature therefore the}$ $\text{electric fields do not form closed loops.}$ $\text{Gauss law is used only in the symmetric configuration computation of an}$ $\text{electric field.}$ $\text{The electrostatic field lines originate from positive charges and terminate on}$ $\text{negative charges. They never form closed loops because the electric field is}$ $\text{conservative, meaning there is no net work done in moving a test charge}$ $\text{along a closed path in the field.}$ $\text{Gauss's law is most useful in systems that have a high degree of symmetry}$ $\text{(e.g., spherical, cylindrical, or planar symmetry). In systems without}$ $\text{symmetry, it is difficult to apply Gauss's law effectively to calculate the}$ $\text{electric field.}$ $\text{Therefore, Statement I is correct, but Statement II is incorrect.}$ $\text{Hence, option (1) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

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
}