Import Question JSON

Current Question (ID: 16456)

Question:

$\text{A hollow metal sphere of radius } R \text{ is uniformly charged. The electric field due to the sphere at a distance } r \text{ from the centre:}$

Options:

1. $\text{decreases as } r \text{ increases for } r < R \text{ and for } r > R.$
2. $\text{increases as } r \text{ increases for } r < R \text{ and for } r > R.$
3. $\text{is zero as } r \text{ increases for } r < R, \text{ decreases as } r \text{ increases for } r > R.$
4. $\text{is zero as } r \text{ increases for } r < R, \text{ increases as } r \text{ increases for } r > R.$

Solution:

$\text{Hint: Use } E_{\text{inside}} = 0$ $\text{Explanation: For the hollow metal sphere, } E_{\text{inside}} = 0 \text{ for } r < R \text{ and } E_{\text{outside}} = \frac{kQ}{r^2} \text{ for } r > R.$ $\text{Hence, option (3) is the correct answer.}$

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
}