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Question

A thin spherical shell of radius 12 cm has \( q = 10 \, \mu\text{C} \). What is the electric field at
14 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: E = (k q/r²) . E = 9 × 10⁹ × (10 × 10⁻⁶/(0.14)²) = 9 × 10⁹ × (10 × 10⁻⁶/0.0196) = 4.59 × 10⁶ N/C . Substituting values gives 4.59 × 10⁶ N/C, which matches expected magnitude for this electrostatic configuration, confirming Coulomb's and Gauss's principles and charge quantization consistency.

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