Practice question
Question
Three charges \( +9 \, \mu\text{C} \), \( -6 \, \mu\text{C} \), and \( +4 \, \mu\text{C} \) are at \(
(0, 0, 0) \), \( (9, 0, 0) \), and \( (0, 9, 0) \, \text{m} \). What is the potential at \( (9, 9, 0) \,
\text{m} \)? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).
Explanation
**Equipotential surface** is surface where V constant, no work done moving charge along it because W = q ΔV =0 when ΔV=0. Electric field E always perpendicular to equipotential surface, direction from higher to lower potential, magnitude E = -dV/dr, steeper potential gradient means stronger field. Distances: r₁ = √(9² + 9²) = 9√(2) m , r₂ = 9 m , r₃ = 9 m . V = 9 × 10⁹ ( (9 × 10⁻⁶/9√(2)) + (-6 × 10⁻⁶/9) + (4 × 10⁻⁶/9) ) . V = 9 × 10⁹ ( (9 × 10⁻⁶/12.728) - (6 × 10⁻⁶/9) + (4 × 10⁻⁶/9) ) . V
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