Eletromagnetismo Teorico-Resolucao Lista de Exercicios sobre Lei de Gauss

022025 Eletromagnetismo teórico TP nº 03 Profa Rosa Batalha Alunos Lucas Magno e Thais Martins 1 Gauss Law S Dds Q div D ρv a D 2xyτz² âx x²z 2xy ây x²y âz D x Dx y Dy z Dz 2yz 2x 0 233 1 2 2 10 b D 2ρz² sen² φ âρ ρz² sen 2φ âφ 2ρ²z² sen² φ âz D 1ρ ρ ρDρ 1ρ φ Dφ sen 2φ z 2ρ² sen² φ 1ρ ρ 2ρz² sen² φ 1ρ φ ρz² icos2φ z 2ρ² sen² φ 41² sen² 110 1² cos 2110 2 1² sen² 110 906 c D 1r² r r² Dr 1r senθ θ senθ Dθ 1r senθ φ Dφ 1r² r 2r senθ cos φ r² 1r senθ θ r cos φ cos θ sen θ 1r senθ φ r sen θ 1r² 6r² sen θ cos φ 1r sen θ r cos φ cos 2θ 2 1r senθ r cos θ 6 sen θ cos φ cos 2θ cos φ sen θ cos θ sen θ 6 sen 30 sen 50 cos 60 cos 50 cos 50 sen 30 128 2 a D 4xyz âx 2x²z ây 2x² y z² âz div D x Dx y Dy z Dz div D 4yz âx 0 ây 4x² yz² âz 4yz âx 0 ây 4x² y z² âz 4yz âx 4x² yz² âz 4yz x² z² CADERNO INTELIGENTE b 7 sen θ âρ z cos φ âφ ρ sen φ âz div D 1ρ ρ ρDρ 1ρ φ Dφ z Dz div D 0 âρ 0 âφ 0 âz 0 c D sen θ sen φ âr cos θ sen φ âθ cos φ âφ div D 1r² r r² Dr 1r sen θ θ Dθ sen θ 1r sen θ φ Dφ div D 0 âr 0 âθ 0 âφ 0 3 densidade de fluxo elétrico D N0 âρ z âz Cm² a D 7ρ âρ z âz Cm² ϕ S Dds ds ρdθ dρ dz âρ Ddσρ 7ρ âρ z âz ρ dρ d z âρ 7ρ² dρ dz S 0 θ 2π 55 z 55 ϕ 02π 5555 7ρ² dz dθ 2π7 14² 2 30184 π b D 7ρ âρ z âz div D 1ρ ρ ρDρ φ Dφ z Dz div D 1ρ 14ρ 1 div D 14 1 15 c S Dds div D dv S Dds SL Dds ST Dds SD Dds SR Dds SR Dds ST 0 θ 2π 0 ρ 14 Dds âz 7ρ âρ z âz ρ dρ d z âz z ρ dρ d θ ztop55 CADERNO INTELIGENTE 02π 014 z ρ dρ dθ zθ ₀2π ρ²2 ₀14 55 2π 14² 2 1078 π SD Dds SD 0 θ 2π 0 ρ 14 SD Dds z ρ dθ zz 55 0π 014 z ρ dθ dθ z 2π ρ²2 ₀14 55 2π 14² 2 1078 π S Dds 30184 π 1078 π 1078 π 32340 π v div D dv v 0 z 11 0 ρ 14 0 θ 2π 02π 014 011 15 ρ d ρ d z dθ 15 θ ₀2π z ₀11 ρ²2 ₀14 32340 π 4 a Q 01 0π 50 ε0 ρ ρ d θ dz Q 50 ε0 2π 2 h ds Qa 50 ε0 2π 2 h 2 π 21x103 2 h 50 ε0 21x103 2107 x 109 Cm² b ρ 4ε 28 mm D ε0E D 8854 x 1012 50 29x103 1581 x 109 Cm² c ϕ S Dds S 0ds 0 CADERNO INTELIGENTE 5 25 x y z 50 cm D Nz2yz âx xz ây xyz2 âz cm2 Nz2x âx dy dz âx 7 zy dy dz 025 05 05 025 7 zy dy dz 7 z22 y22 05 025 05 025 00615 Ôdes D dŝ D dy dz âx 00615 Ôeq D ds D dx dz ây D ds Nz2yz âx xz ây xyz2 âz dy dz ây Nz2 xz dx dz Nz x dx dz 025 050 025 050 Nz x dz dx 7 q22 x22 050 025 05 025 00615 Dr1 D dŝ D dx dz âz 00615 Dr2 D ds D dx dy âz D ds Nz2yz âx xz ây xyz2 âz dx dy âz Nz2xy dx dy Nxy2 dx dy 05 025 05 025 Nz xy dx dy 705 y22 05 025 y22 025 0123 05 025 05 025 D ds D dx dy âz D ds Nz2xy âz dx dy âz Nxyz dx dy 05 025 05 025 Nz xy dx dy 7 x22 y22 05 025 05 025 0246 Σfices 00615 00615 00615 00615 0123 0246 0123 D Nz3 xy Dxz N2 xy D dv 025 05 025 05 025 05 7 xyz2 dx dy dz 7 q22 y22 025 05 025 05 025 05 1z 025 0123 CADERNO INTELIGENTE 6 a σV56 x 106 cm2 Q 0005 0008 ρV 4πr2 dr 56 x 106 4π r33 0005 0008 9078 pC b r 0008 m D Q4πr2 âr D 9078 x 10124π00082 112876 x 109 cm2 c r 0017 m D 9078 x 1012 4π 00192 25 x 109 cm2 CADERNO INTELIGENTE