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Unformatted text preview: Lecture 51 Proof of the Shell Theorem Part I • By symmetry, the electric field must only depend on r and is along a radial line everywhere. •Apply Gauss’s law to the blue surface , we get 2 2 (4 ) 1 4 Q E r Q E r π ε π ε ⋅ = ∴ = Electric Field Outside a uniformly charged thin shell Lecture 52 Shell Theorem Part II •By symmetry, the electric field must only depend on r and is along a radial line everywhere. •Apply Gauss’s law to the blue surface , we get E = 0 . E = 0 inside Discontinuity in E • Equal and opposite contributions from charges on diagonally opposite surface elements. Electric Field Outside a uniformly charged thin shell Lecture 53 Electric Field of a Uniformly Charged Sphere Apply Gauss’s Law directly or use superposition of the shell results Lecture 54 Infinitely long uniformly charged line ( ) ( ) ( ) 2 E endcaps side side E rh π Φ =Φ +Φ =Φ = ⋅ r h Gauss’s Law: enc Q h λ ε ε = 2 2 k E r r λ λ π ε = = Same result but much less work! E Lecture 55 Uniformly charged thin, infinite sheet σ A h Gauss’s Law! ( ) ( ) ( )...
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This note was uploaded on 04/07/2008 for the course PHYS 241 taught by Professor Wei during the Spring '08 term at Purdue.
 Spring '08
 Wei
 Charge

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