exam 1 spring 2006-1

Exam 1 spring 2006-1 - FORMULA SHEET ˆ encl S D ndS Q ⋅ = Ñ 29 29 2 ˆ 4 v V r E r R dV R ρ πε = F qE = dq i dt = ˆ S i J n dS = ⋅

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Unformatted text preview: FORMULA SHEET ˆ encl S D ndS Q ⋅ = ∫ Ñ ( 29 ( 29 2 ' ˆ ' 4 v V r E r R dV R ρ πε = ∫ F qE = dq i dt = ˆ S i J n dS = ⋅ ∫ v J v ρ = B AB A V E dr = ⋅ ∫ ( 29 ( 29 PE r q r C = Φ + dS d dz dV d d dz ρ φ ρ ρ φ = = 2 2 sin sin dS r d d dV r dr d d θ θ φ θ θ φ = = ˆ ˆ ˆ ˆ ˆ ˆ sin dr z dz d d dr r dr r d r d ρ ρ φ ρ φ φ θ φ θ θ = + + = + + 1 TABLE OF INTEGRALS ( 29 ( 29 2 2 1/ 2 2 2 ln dx x x a x a = + + + ∫ ( 29 3/ 2 2 2 2 2 2 dx x a x a x a = + + ∫ ( 29 3/ 2 2 2 2 2 1 x dx x a x a- = + + ∫ ( 29 2 2 1/ 2 2 2 x dx x a x a = + + ∫ ( 29 ( 29 2 2 2 3/ 2 2 2 2 2 ln x dx x x x a x a x a- = + + + + + ∫ ( 29 ( 29 2 2 2 2 2 2 1/ 2 2 2 ln 2 2 x dx x x a a x x a x a + =- + + + ∫ ( 29 ( 29 3/ 2 5/ 2 2 2 2 2 1 5 x x a dx x a + = + ∫ ( 29 ( 29 ( 29 3/ 2 2 2 2 2 2 3/ 2 2 2 4 2 2 3 3 ln 4 8 8 x x a a x x a x a dx a x x a + + + = + + + + ∫ 2 TABLE OF COORDINATE SYSTEM FORMULAS cos x ρ φ = ˆ ˆ sin cos / x r θ φ ⋅ = = r x sin y ρ φ = ˆ ˆ...
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This note was uploaded on 10/29/2009 for the course ECE 2317 taught by Professor Staff during the Spring '08 term at University of Houston.

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Exam 1 spring 2006-1 - FORMULA SHEET ˆ encl S D ndS Q ⋅ = Ñ 29 29 2 ˆ 4 v V r E r R dV R ρ πε = F qE = dq i dt = ˆ S i J n dS = ⋅

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