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Practice question

MCQ

Question

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

Options

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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 = √((3-0)² + (4-0)²) = 5 m , r₂ = 4 m , r₃ = 3 m . V = 9 × 10⁹ ( (3 × 10⁻⁶/5) + (-2 × 10⁻⁶/4) + (4 × 10⁻⁶/3) ) . V = 9 × 10⁹ ( 0.6 × 10⁻⁶ - 0.5 × 10⁻⁶ + 1.33 × 10⁻⁶ ) = 9

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