Import Question JSON

Current Question (ID: 16449)

Question:

$\text{Two-point charges, } +q \text{ and } -q \text{ are held fixed at } (-d, 0) \text{ and } (d, 0) \text{ respectively of an } (x, y) \text{ coordinate system. Then:}$

Options:

1. $E \text{ at all points on the } y\text{-axis is along } \hat{i}.$
2. $\text{The electric field } \vec{E} \text{ at all points on the } x\text{-axis has the same direction.}$
3. $\text{Dipole moment is } 2qd \text{ directed along } \hat{i}.$
4. $\text{Work has to be done in bringing a test charge from infinity to the origin.}$

Solution:

$\text{(1) From the figure, it is clear that } \vec{E} \text{ at all points on the } y\text{-axis is along } \hat{i}.$ $\text{Here } \vec{E} \text{ of all points on the } x\text{-axis cannot have the same direction.}$ $\text{Here electric potential at origin is zero so no work is done in bringing a test charge from infinity to origin.}$ $\text{Here the dipole moment is in the } -x\text{-direction (} -q \text{ to } +q).$ $\text{Hence only option (1) is correct.}$

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
}