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Current Question (ID: 16533)

Question:

$\text{A conducting sphere of radius } R \text{ is given a charge } Q. \text{ The electric potential and field at the centre of the sphere respectively are:}$

Options:

1. $\text{Zero and } \frac{Q}{4\pi\varepsilon_0 R^2}$
2. $\frac{Q}{4\pi\varepsilon_0 R} \text{ and zero}$
3. $\frac{Q}{4\pi\varepsilon_0 R} \text{ and } \frac{Q}{4\pi\varepsilon_0 R^2}$
4. $\text{Both are zero}$

Solution:

$\text{Hint: The whole charge resides on the surface of the conducting sphere.}$ $\text{Step: Find the electric field and the potential at the centre of the sphere.}$ $V = \frac{KQ}{R} = \frac{Q}{4\pi\varepsilon_0 R}$ $\text{The electric potential is the same for the whole conducting sphere i.e.,}$ $\text{The electric field at the centre of any conducting sphere due to a charge on the surface of the sphere would be zero.}$ $\text{Therefore, for a conducting sphere, the electric field at the centre } = 0$ $\text{Hence, option (2) is the correct answer.}$

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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
}