Lecture_08_part02

Lecture_08_part02 - Spherical Shell of Charge Field inside...

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Field inside: E =0 Field outside: r r Q E ˆ 4 1 2 0 πε = (like point charge) Spherical Shell of Charge

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What if charges are distributed throughout an object? Step 1: Cut up the charge into pieces r E R For each sphere: r r dQ E d ˆ 4 1 2 0 πε = outside: inside: dE = 0 Outside a solid sphere of charge: r r Q E ˆ 4 1 2 0 πε = for r>R A Solid Sphere of Charge
Inside a solid sphere of charge: E r r Q E ˆ 4 1 2 0 Δ = πε Δ Q = Q (volume of inner shells) (volume of sphere) Δ Q = Q 4 / 3 π r 3 4 / 3 π R 3 = Q r 3 R 3 R r E = 1 4 πε 0 Qr R 3 ˆ r for r<R Why is E~r ? On surface: E = 1 4 πε 0 QR R 3 ˆ r = 1 4 πε 0 Q R 2 ˆ r A Solid Sphere of Charge

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Δ Q Mathematical idealization Charge distribution is not continuous Charge distribution is not exactly uniform Works well for macroscopic systems Atomic force microscope: scans microscopic structure using variations in charge density on surface Infinitesimals and Integrals in Science
Chapter 16 Electric Potential

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