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Current Question (ID: 16393)

Question:

$\text{Two charges } 2 \, \mu\text{C and } 8 \, \mu\text{C are separated by } 6 \, \text{cm. The neutral point is at:}$

Options:

1. $4 \, \text{cm from } 2 \, \mu\text{C.}$
2. $2 \, \text{cm from } 2 \, \mu\text{C.}$
3. $2 \, \text{cm from } 8 \, \mu\text{C.}$
4. $3 \, \text{cm from } 8 \, \mu\text{C.}$

Solution:

$\text{Hint: } F = \frac{k q_1 q_2}{r^2}$ $\text{Step: Find the neutral point at two charges } 2 \, \mu\text{C and } 8 \, \mu\text{C are separated by } 6 \, \text{cm.}$ $\text{The force on } q \text{ due to } 2 \, \mu\text{C charge is given by:}$ $F_1 = \frac{k \times (2 \, \mu\text{C}) q}{x^2}$ $\text{The force on } q \text{ due to } 8 \, \mu\text{C charge is given by:}$ $F_2 = \frac{k \times (8 \, \mu\text{C}) q}{(6-x)^2}$ $\text{At the neutral point, } F_1 = F_2$ $\frac{k \times (2 \, \mu\text{C}) q}{x^2} = \frac{k \times (8 \, \mu\text{C}) q}{(6-x)^2}$ $\Rightarrow 4x^2 = (6-x)^2$ $\Rightarrow 2x = 6-x \quad [\text{taking square root both sides}]$ $\Rightarrow x = 2 \, \text{cm} \quad (\text{from } 2 \, \mu\text{C charge})$ $\text{Hence, option (2) is the correct answer.}$

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
}