Import Question JSON

Current Question (ID: 20048)

Question:

$\text{A charge of } 10 \, \mu\text{C is placed at the origin. Where should a charge of } 40 \, \mu\text{C be placed on the } x\text{-axis so that the electric field at } x = 2 \text{ units is zero?}$

Options:

1. $-2 \text{ units}$
2. $4 \text{ units}$
3. $6 \text{ units}$
4. $2 \text{ units}$

Solution:

$\text{Hint: } E = \frac{kQ}{r^2}$ $\text{Step: Find the position of charge } 40 \, \mu\text{C on the } x\text{-axis.}$ $\text{The direction of the electric field on both charges at the point } P \text{ is shown in the figure below;}$ $\text{The electric field due to the charge } 10 \, \mu\text{C is given by:}$ $E = \frac{k \times 10}{2^2}$ $\text{The electric field due to the charge } 40 \, \mu\text{C is given by:}$ $E = \frac{k \times 40}{(x_0 - 2)^2}$ $\text{For the electric field to be zero:}$ $\frac{1}{4\pi\varepsilon_0} \times \frac{10}{2^2} = \frac{1}{4\pi\varepsilon_0} \times \frac{40}{(x_0 - 2)^2}$ $\Rightarrow x_0 - 2 = 4$ $\Rightarrow x_0 = 6 \text{ units}$ $\text{Hence, option (3) is the correct answer.}$

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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
}