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Answer :
vThe electric potential (\(V\)) at a distance \(r\) along the axis of a short dipole with dipole moment (\(p\)) can be calculated using the formula:
\[ V = \frac{1}{4\pi\epsilon_0} \frac{p \cos(\theta)}{r^2} \]
Where:
- \( \epsilon_0 \) is the vacuum permittivity (approximately \(8.85 \times 10^{-12} \, \text{C}^2/\text{N}\cdot\text{m}^2\))
- \( p \) is the dipole moment (given in coulomb-meters)
- \( r \) is the distance from the dipole along its axis
In this case, \( p \) is given in coulomb-meters. Let's assume \( p = p_0 \, \text{C} \cdot \text{m} \).
We can also assume that the dipole is oriented along the z-axis, so \( \theta = 0^\circ \), and \( \cos(\theta) = 1 \).
Given that \( r = 3 \) meters, we can calculate \( V \):
\[ V = \frac{1}{4\pi \times 8.85 \times 10^{-12}} \frac{p_0 \times 1}{3^2} \]
\[ V = \frac{1}{4\pi \times 8.85 \times 10^{-12}} \frac{p_0}{9} \]
Let's calculate the value of \( V \)
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