Exam_1_Cribsheet

# Exam_1_Cribsheet - Crib Sheet for Exam#1 Current I = J dS =...

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Crib Sheet for Exam #1 Current ˆ V SS S I dd S d =⋅ = ∫∫ JS Jn vS ρ Point form of Coulomb’s law (force on 2 q due to 1 q ) 12 2 ˆ [N] 4 qq R πε = FR , where 21 R =− rr , ˆ R = R Electric field and electric flux density q = F E , 0 = DE ε [C/m 2 ] , 9 0 1 10 36 π ≈× [F/m] 22 2 2 1 0 ˆˆ ˆ () ˆ 444 4 N nV s n n n Vs q dV dS d RR = ′′ === = rR ER A A A ρρ [V/m] , where R , ˆ R = R Gauss’ law ˆ net S dS Q ⋅= Dn v Useful coordinate system identities ˆ sin cos ˆ ˆ ˆ cos sin ˆ cos sin ˆ sin cos θ θθ φφ φ =+ + r ρ z θρ z ρ x y φ x y cos sin cos sin sin sin cos xr yr zr φθ = = == = ˆ d d z ρφ + z A ˆ sin d r d θφ + r A z dS d dz dS d dz dS d d = = = ρρφ 2 sin sin r dS r d d dS r dr d dS rdrd = = = θθφ dV d d dz = 2 sin dV r dr d d =

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Useful Integral Expressions () ( ) 22 ln dx x xa =+ + + xdx x a + 1 1 tan dx x aa  =   + 1 ln 2 x a + 3/2 22 2 dx x ax a = + + 1 x a = + + 1 ax ax e xe dx x =− 2 ax ax ex xed x x a + ( ) 2 ln xd x x x + + + + 1 sin ( ) sin (
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## This note was uploaded on 10/25/2011 for the course ECE 2317 taught by Professor Staff during the Fall '08 term at University of Houston.

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Exam_1_Cribsheet - Crib Sheet for Exam#1 Current I = J dS =...

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