Practice question
Question
Two charges \( 10 \, \mu\text{C} \) and \( -2 \, \mu\text{C} \) are at \( (8, 0, 0) \) and \( (-8, 0,
0) \, \text{cm} \). What is the potential at midpoint? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times
10^9 \, \text{Nm}^2 \text{C}^{-2} \)).
Explanation
**Spherical conductor** behaves as point charge outside, potential V = k Q/R at surface, field E = k Q/r² for r>R, zero inside for rR, so E = k Q/r² =9×10⁹×6×10⁻⁸/0.16=3375 N/C. Distance to midpoint = 0.08 m. V = 9 × 10⁹ ( (10 × 10⁻⁶/0.08) + (-2 × 10⁻⁶/0.08) ) = 9 × 10⁹ × (8 × 10⁻⁶/0.08) . V = 9 × 10⁹ × (8 × 10⁻⁶/0.08) = 9 × 10⁵ V . Using V = kQ/r, U = k q₁q₂/r, E = -dV/dr, C = ε₀A/d, 1/C_eq series, C_eq =
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