Import Question JSON

Current Question (ID: 20056)

Question:

$x = 2.$ $\text{Two-point charges each of magnitude } q \text{ is kept at a separation of } 2a.$ $\text{The distance from mid-point on perpendicular bisector where a point charge will experience maximum force is } \frac{a}{\sqrt{x}}.$ $\text{Then } x =$

Options:

1. 3
2. 2 (Correct)
3. 1
4. 4

Solution:

$\text{Step 1: Draw the diagram.}$ $\text{Step 2: Find the net electric field at the point } P.$ $E_{\text{net}} = 2E \cos \alpha$ $\Rightarrow E_{\text{net}} = 2 \times \frac{Kq}{a^2 + y^2} \times \frac{y}{\sqrt{a^2 + y^2}}$ $\Rightarrow E_{\text{net}} = \frac{2Kq}{(a^2 + y^2)^{3/2}}$ $\text{Step 3: Find the value of } x.$ $\text{For the maximum force:}$ $\frac{dF}{dy} = 0$ $\Rightarrow \frac{d(qE_{\text{net}})}{dy} = 0$ $\Rightarrow \frac{dE_{\text{net}}}{dy} = 0$ $\Rightarrow y = \frac{a}{\sqrt{2}}$ $\text{Hence, option (2) is the correct answer.}$

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
}