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Current Question (ID: 16437)

Question:

$\text{An electric dipole is placed at an angle of } 30^\circ \text{ with an electric field intensity } 2 \times 10^5 \text{ N/C.}$ $\text{It experiences a torque equal to } 4 \text{ N-m.}$ $\text{The charge on the dipole, if the dipole length is } 2 \text{ cm, is:}$

Options:

1. $8 \text{ mC}$
2. $2 \text{ mC}$
3. $5 \text{ mC}$
4. $7 \mu\text{C}$

Solution:

$\text{Hint: Torque on a dipole in an electric field, } \vec{\tau} = \vec{p} \times \vec{E}$ $\Rightarrow |\tau| = pE \sin \theta$ $\text{Step 1: Use the above relation to find the dipole moment.}$ $\vec{\tau} = \vec{p} \times \vec{E} \Rightarrow |\tau| = pE \sin \theta$ $4 = p(2 \times 10^5) \times \frac{1}{2}$ $\text{Or, } p = 4 \times 10^{-5}$ $\text{Step 2: Use the formula of dipole moment to find the charge.}$ $p = 2qd$ $\Rightarrow q = \frac{4 \times 10^{-5}}{2 \times 10^{-2}} = 2 \text{ mC}$

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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
}