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Question

Two charges \( +10 \, \mu\text{C} \) and \( -2 \, \mu\text{C} \) are 80 cm apart. What is the distance
from \( +10 \, \mu\text{C} \) where the electric field is zero?

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Explanation

**Quantization of charge** states observable charge is integer multiple of elementary charge e = 1.6×10⁻¹⁹ C, q = n·e, and total charge is conserved in isolated systems. Loss of electrons produces positive charge, and number of transferred electrons follows n = q/e, linking macroscopic charge measurement to microscopic carriers. Let x be distance from +10 μC , then 0.8 - x from -2 μC . (10 × 10⁻⁶/x²) = (2 × 10⁻⁶/(0.8 - x)²) , 10 (0.8 - x)² = 2 x² . 5 (0.64 - 1.6 x + x²) = x² , 3.2 - 8 x + 5 x² = x² . 4 x²

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