Import Question JSON

Current Question (ID: 20073)

Question:

$\text{Four point charges } -q, +q, +q \text{ and } -q \text{ are placed on } y\text{-axis at } y = -2d, y = -d, y = +d, y = +2d, \text{ respectively. The magnitude of the electric field } E \text{ at a point a the } x\text{-axis at } x = D, \text{ with } D >> d, \text{ will behave as:}$ $1. \ E \propto \frac{1}{D}$ $2. \ E \propto \frac{1}{D^3}$ $3. \ E \propto \frac{1}{D^4}$ $4. \ E \propto \frac{1}{D^2}$

Options:

1. $E \propto \frac{1}{D}$
2. $E \propto \frac{1}{D^3}$
3. $E \propto \frac{1}{D^4}$
4. $E \propto \frac{1}{D^2}$

Solution:

$\text{Hint: Vertical component of electric field is zero.}$ $E_p = \frac{2E_1 \cos \theta_1 - 2E_1 \cos \theta_2}{\frac{2Kq}{d^2 + D^2}} \times \frac{D}{(d^2 + D^2)^{3/2}} - \frac{2Kq}{(2d)^2 + D^2} \times \frac{1}{[2d]^2}$ $= 2KqD \left[ d^2 + D^2 \right]^{-3/2} - (4d^2 + D^2)$ $= \frac{2Kq}{D^2} \left( 1 - \frac{3}{2} \frac{d^2}{D^2} - 1 - \frac{3 \times 4d}{2D^2} \right)$ $= \frac{9Kqd^2}{D^4}$

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
}