Practice question
Question
Three charges \( +8 \, \mu\text{C} \), \( -5 \, \mu\text{C} \), and \( +3 \, \mu\text{C} \) are at \(
(0, 0, 0) \), \( (8, 0, 0) \), and \( (0, 8, 0) \, \text{m} \). What is the potential at \( (8, 8, 0) \,
\text{m} \)? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).
Explanation
**Electric potential** V = k Q/r, k = 1/(4π ε₀)=9×10⁹ N·m²/C², Q charge (C), r distance (m), scalar, potential at surface of spherical conductor radius R, V = k Q/R. Potential difference ΔV = V_B - V_A = -∫ E·dl, work per unit charge to move charge without acceleration. Distances: r₁ = √(8² + 8²) = 8√(2) m , r₂ = 8 m , r₃ = 8 m . V = 9 × 10⁹ ( (8 × 10⁻⁶/8√(2)) + (-5 × 10⁻⁶/8) + (3 × 10⁻⁶/8) ) . V = 9 × 10⁹ ( (8 × 10⁻⁶/11.314) - (5 × 10⁻⁶/8) + (3 × 10⁻⁶/8)
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