Import Question JSON

Current Question (ID: 20042)

Question:

$\text{The three charges } \frac{q}{2}, q \text{ and } \frac{q}{2} \text{ are placed at the corners } A, B \text{ and } C$ $\text{of a square of side } a \text{ as shown in the figure. The magnitude of the}$ $\text{electric field } (E) \text{ at the corner } D \text{ of the square is:}$

Options:

1. $\frac{q}{4\pi\varepsilon_0 a^2} \left( \frac{1}{\sqrt{2}} + \frac{1}{2} \right)$
2. $\frac{q}{4\pi\varepsilon_0 a^2} \left( 1 + \frac{1}{\sqrt{2}} \right)$
3. $\frac{q}{4\pi\varepsilon_0 a^2} \left( 1 - \frac{1}{\sqrt{2}} \right)$
4. $\frac{q}{4\pi\varepsilon_0 a^2} \left( \frac{1}{\sqrt{2}} - \frac{1}{2} \right)$

Solution:

$\text{Hint: } E = \frac{kq}{r^2}$ $\text{(E}_{\text{net}})_{D} = \frac{kq}{2a^2} + \frac{\sqrt{2}kq}{2a^2}$ $\text{(E}_{\text{net}})_{D} = \frac{kq}{a^2} \left( \frac{1}{2} + \frac{1}{\sqrt{2}} \right)$ $\text{(E}_{\text{net}})_{D} = \frac{q}{4\pi\varepsilon_0 a^2} \left( \frac{1}{2} + \frac{1}{\sqrt{2}} \right)$

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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
}