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Current Question (ID: 20023)

Question:

$\text{Shown in the figure is a shell made of a conductor. It has inner radius } a \text{ and outer radius } b, \text{ and carries charge } Q. \text{ At its centre is a dipole } \vec{p} \text{ as shown. In this case:}$

Options:

1. $\text{surface charge density on the inner surface is uniform and equal to } \frac{(Q/2)}{4\pi a^2}$
2. $\text{surface charge density on the outer surface depends on } |\vec{p}|$
3. $\text{surface charge density on the inner surface of the shell is zero everywhere}$
4. $\text{the electric field outside the shell is the same as that of a point charge at the centre of the shell}$

Solution:

$\text{Hint: So for any observer outside the shell, the resultant electric field is due to } Q \text{ uniformly distributed on the outer surface only.}$ $\text{The charge distribution at equilibrium on the conductor will be like:}$ $\text{Net charge on the outer surface } = Q$ $\text{Total charge on the inner surface } = 0$ $\text{So for any observer outside the shell, the resultant electric field is due to } Q \text{ uniformly distributed on the outer surface only.}$

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
}