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Current Question (ID: 20092)

Question:

$\text{A charge of } 10 \, \mu\text{C is split into two equal parts, and the resulting charges are placed } 1 \, \text{cm apart. What will be the force of repulsion between the two charges?}$

Options:

1. $225 \, \text{N}$
2. $450 \, \text{N}$
3. $2250 \, \text{N}$
4. $4500 \, \text{N}$

Solution:

$\text{Hint: } F = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r^2}$ $\text{Step: Find the repulsive force between the charges.}$ $\text{If two point charges } q_1, q_2 \text{ are separated by a distance } r \text{ in a vacuum, then the magnitude of the force } (F) \text{ between them is given by:}$ $F = \frac{1}{4\pi\varepsilon_0} \frac{q_1 q_2}{r^2}$ $\Rightarrow F = \frac{9 \times 10^9 \times (5 \times 10^{-6})^2}{(10^{-2})^2} = 9 \times 25 \times 10 = 2250 \, \text{N}$ $\text{Therefore, the repulsive force between the charges is } 2250 \, \text{N.}$ $\text{Hence, option (3) is the correct answer.}$

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
}