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Question

A thin spherical shell of radius 12 cm has a total charge of \( 9 \, \mu\text{C} \). What is the
electric field at 15 cm from the center?

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Explanation

**Symmetric configurations** from Gauss's law produce characteristic fields. Uniformly charged infinite plane gives uniform field E = σ/(2ε₀) independent of distance due to planar symmetry, spherical shell acts as point charge outside E = kq/r² and zero inside, reflecting zero enclosed charge interior. Outside shell ( r > R ): E = (k q/r²) . k = 9 × 10⁹ N·m²/C² , q = 9 × 10⁻⁶ C , r = 0.15 m . E = 9 × 10⁹ × (9 × 10⁻⁶/(0.15)²) = 9 × 10⁹ × (9 × 10⁻⁶/0.0225) = 3.6 × 10⁶ N/C . Substituting values gives 3.6 × 10⁶ N/C, which

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