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Question

A thin spherical shell of radius 8 cm has \( q = 4 \, \mu\text{C} \). What is the electric field at 10
cm from the center?

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Explanation

**Special distributions** like infinite line, plane, spherical shell demonstrate Gauss's law advantage. Outside shell, charge appears concentrated at centre; inside, q_enc = 0 implies vanishing field, key result for shielding. Outside shell: E = (k q/r²) . E = 9 × 10⁹ × (4 × 10⁻⁶/(0.1)²) = 9 × 10⁹ × (4 × 10⁻⁶/0.01) = 3.6 × 10⁶ N/C . Substituting values gives 3.6 × 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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