Import Question JSON

Current Question (ID: 16529)

Question:

$\text{An electric dipole has the magnitude of its charges as } q \text{ and its dipole moment is } p. \text{ It is placed in a uniform electric field } \mathbf{E}. \text{ If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively:}$

Options:

1. $q \cdot E \text{ and } p \cdot E$
2. $\text{zero and minimum}$
3. $q \cdot E \text{ and maximum}$
4. $2q \cdot E \text{ and minimum}$

Solution:

$\text{When the electric dipole is placed in a uniform electric field, the net force acting on the dipole is equal to zero.}$ $u = -\mathbf{p} \cdot \mathbf{E} = -pE \cos \theta = -pE \cos 0^\circ = -pE \text{(minimum)}$

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
}