Import Question JSON

Current Question (ID: 20091)

Question:

$\text{An electric dipole with a dipole moment of } 5 \, \mu\text{C-m is placed in a uniform electric field of } 600 \, \text{N/C, at an angle of } 90^\circ \text{ to the direction of the field. The torque experienced by the dipole, (in milli-Newton-meters) is equal to:}$

Options:

1. $3$
2. $0$
3. $0.3$
4. $30$

Solution:

$\text{Hint: } \tau = |\vec{p} \times \vec{E}|$ $\text{Step: Find the value of torque experienced by the dipole.}$ $\text{The torque experienced by the dipole is given by;}$ $\tau = pE \sin \theta$ $\Rightarrow \tau = 5 \times 10^{-6} \, \text{C-m} \times 600 \, \text{N/C} \sin 90^\circ$ $\Rightarrow \tau = 5 \times 10^{-6} \, \text{C-m} \times 600 \, \text{N/C} \sin 90^\circ$ $\Rightarrow \tau = 3000 \times 10^{-6} \, \text{N-m}$ $\Rightarrow \tau = 3 \times 10^{-3} \, \text{N-m}$

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
}