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Current Question (ID: 16512)

Question:

$\text{Equipotential at a great distance from a collection of charges whose total sum is not zero are approximately:}$

Options:

1. $\text{spheres}$
2. $\text{planes}$
3. $\text{paraboloids}$
4. $\text{ellipsoids}$

Solution:

$\text{(A) Hint: For greater distance, the collection of charges can be considered as a point charge.}$ $\text{Step 1:}$ $\text{The equipotentials due to a collection of charges for greater distance are spherical in shape as electric potential due to a collection of charges is given by,}$ $V = K \frac{q}{r}$ $\text{Step 2:}$ $\text{This suggests that electric potential due to a point charge is same for all equidistant points. The locus of these equidistant points, which are at the same potential, form a spherical surface.}$

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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
}