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Current Question (ID: 16530)

Question:

$\text{A short electric dipole has a dipole moment of } 16 \times 10^{-9} \text{ C-m. The electric potential due to the dipole at a point at a distance of } 0.6 \text{ m from the centre of the dipole situated on a line making an angle of } 60^\circ \text{ with the dipole axis is:}$ $\left( \frac{1}{4\pi\varepsilon_0} = 9 \times 10^9 \text{ N-m}^2/\text{C}^2 \right)$

Options:

1. $200 \text{ V}$
2. $400 \text{ V}$
3. $\text{zero}$
4. $50 \text{ V}$

Solution:

$\text{Hint: Apply } V(r) = \frac{k(\vec{p} \cdot \vec{r})}{r^3}$ $\text{Step: Find the electric potential due to the electric dipole.}$ $\text{The general formula for the electric potential for an electric dipole at a point}$ $\text{situated at distance, } 'r' \text{ from the midpoint of the dipole and making an angle}$ '$\theta' \text{ from the axis of the dipole is given by;}$ $V(r) = \frac{k(\vec{p} \cdot \vec{r})}{r^3} \Rightarrow V = \frac{1}{4\pi\varepsilon_0} \times \frac{p \cos \theta}{r^2}$ $\text{Substitute the known values we get;}$ $\Rightarrow V = 9 \times 10^9 \times \frac{16 \times 10^{-9} \times \frac{1}{2}}{0.6 \times 0.6}$ $\Rightarrow V = \frac{72}{36} \times 100 = 200 \text{ V}$ $\text{Hence, option (1) is the correct answer.}$

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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
}