P260sheet - Ch. 21 1 Coulomb's law: F = k qrq2 r, k = 2 ^...

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Ch. 21 Coulomb’s law: ~ F = k q 1 q 2 r 2 ˆ r , k = 1 4 π± 0 E = F q , so dE = k ˆ rdq r 2 Given uniform charge density: dq = Q V dV = ρdV for a volume, σdA for a sheet, λdl for a line Dipoles For q at ~ d and - q at 0: ~ P q ~ d . ~ F net = 0 ~ τ = ~ r × ~ F = ~ P × ~ E = PE sin θ U = - ~ P · ~ E Ch. 22 Φ = H ~ E · d ~ A = q encl ± 0 . For a closed surface, ~ A points outward. H is the integral over a closed surface. E ( X ) = 1 ± 0 R X 0 ρ ( x )( x X ) D - 1 dx , where D is the dimen- sion of the symmetry (1 slab, 2 cylindrical, 3 spheri- cal). ring: E = kQx ( x 2 + a 2 ) 3 / 2 (a radius, x distance) line: 1 2 π± 0 λ x x 2 /a 2 +1 (2a length, x distance) line: E = λ 2 π± 0 r sheet: E = σ 2 ± 0 . (Think one end (half) of a Gaus- sian cylinder.) disk: E = σ 2 ± 0 (1 - 1 R 2 /x 2 +1 ) parallel plates: E outside = 0; E between = σ ± 0 insulating sphere: E inside = kQr R 3 A sphere = 4 πr 2 Conductors: A conductor is enclosed by an equipo- tential surface, so E = E at surface. E inside = q inside = 0. Ch. 23 ~ F is a conservative force if W a a = H a a ~ F · d ~ l = 0. W a b is path-independent. ≡ ∃ U : ~ F ( ~ r ) = - ~ U ( ~ r ) U + K is constant Δ U = - W for a slow displacement from rest to rest. U
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This note was uploaded on 04/01/2008 for the course PHYSICS 260 taught by Professor Evrard during the Fall '07 term at University of Michigan.

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P260sheet - Ch. 21 1 Coulomb's law: F = k qrq2 r, k = 2 ^...

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