Import Question JSON

Current Question (ID: 16495)

Question:

$\text{A hollow conducting sphere is placed in an electric field produced by a point charge placed at } P \text{ as shown in the figure. Let } V_A, V_B, V_C \text{ be the potentials at points } A, B \text{ and } C \text{ respectively. Then:}$

Options:

1. $V_A < V_B < V_C$
2. $V_A > V_B > V_C$
3. $V_C > V_B = V_A$
4. $V_A = V_B = V_C$

Solution:

$\text{The potential same for every point of the conducting sphere.}$ $\text{A hollow conducting sphere in an electric field redistributes its charges such that the electric potential becomes the same at all points on and inside the conducting surface. This is a fundamental property of conductors in electrostatic equilibrium: the potential is constant throughout the conductor and on its surface.}$ $\text{Here, } A, B, \text{ and } C \text{ are points on or inside the conducting sphere. Since the sphere is in electrostatic equilibrium, the potential at all these points is the same:}$ $V_A = V_B = V_C$ $\text{Hence, option (4) is the correct answer.}$

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
}