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Question

A thin spherical shell of radius 10 cm has \( q = 8 \, \mu\text{C} \). What is the electric field at 15
cm from the center?

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Explanation

**Field due to infinite plane and shells** illustrates symmetry power. Infinite plane's field remains constant because distant contributions balance, while spherical shell interior field cancels symmetrically, leading to E = 0 inside, E = kQ/r² outside. Outside shell: E = (k q/r²) . E = 9 × 10⁹ × (8 × 10⁻⁶/(0.15)²) = 9 × 10⁹ × (8 × 10⁻⁶/0.0225) = 3.2 × 10⁶ N/C . Substituting values gives 3.2 × 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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