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Question

An electric dipole with moment \( p = 2 \times 10^{-10} \, \text{C m} \) is at the origin, aligned
along the x-axis. What is the potential at \( (0, 2, 0) \, \text{m} \)? (Take \( \frac{1}{4 \pi
\varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

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Explanation

**Equipotential through midpoint** of +q and -q is perpendicular bisector, V=0 everywhere on it because contributions k q/r and k(-q)/r cancel. For two opposite charges, potential at midpoint zero, but field non-zero, pointing from positive to negative, illustrating vector vs scalar nature. Position vector r = (0, 2, 0) , r = 2 m , hatr = (0, 1, 0) . Dipole moment p = (2 × 10⁻¹⁰, 0, 0) . V = (1/4 π ε₀) (p · hatr/r²) = 9 × 10⁹ × ((2 × 10⁻¹⁰) · (0)/2²) = 0 V (since cos θ = 0 , equatorial plane). Using V = kQ/r, U

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