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Question

Two charges \( 6 \, \mu\text{C} \) and \( -3 \, \mu\text{C} \) are at \( (10, 0, 0) \) and \( (-10, 0,
0) \, \text{cm} \). What is the potential at midpoint? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times
10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

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Explanation

**Conductor in electrostatic equilibrium** has E=0 inside, charges reside on surface, potential constant throughout conductor. Hollow shell with no internal charge has zero field inside cavity, even if external field present, charges on outer surface screen interior, principle used in Faraday cage. Distance to midpoint = 0.1 m. V = 9 × 10⁹ ( (6 × 10⁻⁶/0.1) + (-3 × 10⁻⁶/0.1) ) = 9 × 10⁹ × (3 × 10⁻⁶/0.1) = 2.7 × 10⁵ V . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq series, C_eq = ΣC parallel, U = ½ C V² and common potential V

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