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Current Question (ID: 16492)

Question:

$\text{Two equal charges } q \text{ of opposite sign separated by a distance } 2a \text{ constitute an}$ $\text{electric dipole of dipole moment } p. \text{ If } P \text{ is a point at a distance } r \text{ from the}$ $\text{centre of the dipole and the line joining the centre of the dipole to this point}$ $\text{makes an angle } \theta \text{ with the axis of the dipole, then the potential at } P \text{ is given}$ $\text{by: } \left( r \gg 2a \right) , \text{ where } p = 2qa$

Options:

1. $V = \frac{p \cos \theta}{4 \pi \varepsilon_0 r^2}$
2. $V = \frac{p \cos \theta}{4 \pi \varepsilon_0 r}$
3. $V = \frac{p \sin \theta}{4 \pi \varepsilon_0 r}$
4. $V = \frac{p \cos \theta}{2 \pi \varepsilon_0 r^2}$

Solution:

$\text{Hint: } V = \frac{k p \cos \theta}{r^2}$ $\text{Step: Find the potential at } P$ $\text{For the given situation, the diagram can be drawn as follows:}$ $\text{As shown in the figure component of dipole moment along the line } OP \text{ will}$ $\text{be; } p' = p \cos \theta.$ $\text{Hence the electric potential at point } P \text{ will be;}$ $V = \frac{1}{4 \pi \varepsilon_0} \times \frac{p \cos \theta}{r^2}$ $\text{Hence, option (1) is the correct answer.}$

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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
}