Import Question JSON

Current Question (ID: 20146)

Question:

$\text{Given below are two statements:}$ $\text{Statement I:}$ \text{Electric potential is constant within and at the surface of each conductor.}$ $\text{Statement II:}$ \text{An electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.}$

Options:

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

Solution:

$\text{Hint: Electric field is perpendicular to the equipotential surfaces.}$ $\text{Explanation: Inside a conductor in electrostatic equilibrium, the electric field is zero. Since the electric field is the negative gradient of the electric potential } (E = -\Delta V), \text{ this implies that the electric potential must be constant throughout the interior of the conductor. At the surface of the conductor, the electric potential is also constant.}$ $\text{The electric field just outside a conductor is always perpendicular to the surface at every point. This is because the charges on a conductor in electrostatic equilibrium reside only on the surface, and the electric field they generate is directed normal (perpendicular) to the surface.}$ $\text{Therefore, both Statement I and Statement II are correct. Hence, option (1) is the correct answer.}$

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
}