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Engenharia Ambiental e Sanitária ·
Eletromagnetismo
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Lista 3 Q1) E: 8x10^4 V/m d: 0.5mm proton a) ΔV A->B ΔV= -∫ Eo b do ΔV= E0.db ΔV= Eo(0-b) => ΔV= (| ΔV= -8x)) (0.5 .3)6) ====) ΔV= -4x104 ΔV= ΔE (Δ 8'4 1-810\0 (° ) ====> o 1 -08888 - (b) ΔU: =0 proton 16.6x10^-19 9ΔU: ΔU/9 ΔI +866A. A pop (6 ) -0) ΔU 9.=====> 16° 9 => ΔU=6.4 510^ J) Q2) r R1=0.9mm = 0.9x10^-3m R2=2.55mm 2.551x10^-3 | | q4 q3:1mC m: 20mg 209 X 10^-3 | | | ERE+KE+UET Ec= £ 查 (m) CsK.KE+UEDU1=KE+UNa ~ 2-9699(Un)=Uan Un2 | m___m___m\ mv21 U = K90 d ked(Q. o) = Kx9\ | m NO \___p_agebo(\*4-949= ) c=8.999\ | ） q=2\/x10^2|2) 1.9aa=2.955-10 = 1 (...) in V= 2490 mV 2.49 KM) Q3 q1=20mC q2=-20mC q3=10mC d=4cm=0.04m (i) q1 q3 q2 \_|__/=> a) energia potencial no longo d x do eixo x = Vx.q0 a) d V=V1+V2+V3 V1=Kq10mC d V2=K(-20mC) x d V=Kq20mC x x dx9x10 / V23=K(10mC) x 10^-8 x V=U. + 0 6.9 9 U = 0 = V.6 x U=0 36 V=x V=K.q13-V.q01.1 mmh V: K.q13_6m Q4 V=K.qdcosΘ r^2 p .X....p(f) |y || y | z V(K x n^2 + znK) p(x) | K z_eq = 0 Kp x-KRpf\ z n^3 | R^2 = x^2+ -> \ V k00 / (x2^2+z2^2) y + 0+ \n(-> : E(-A): E(r)/_F )-_3 & Belly \ \[ r(s)\ F/() 'xp('/)( /df+r)\ ///="V( gx \ / dyy\ O py+ (x^2+z2^2(3/2) A(p)(3xp^2IdentityP (+z( x16822 ) X Q18 A: 42cm^2 d: 1,3mm DV=625V a) E= EA / d 42 x (10^-4) / 1,3 x 10^-3 E= 8,85x10^-12 x 4,2 x 10^3 => C= 98,59 x 10^-12 F b) C= Q / DV => 98,59 x 10^-12 x 625= Q => Q= 17,86 x 10^-9 c) U= 1/2 C (DV)^2 => U= 98,59 x 10^-12 x 625^2 / 2 U= 5,58 x 10^-5 J d) E= V / d => 625 / 1,3 x 10^-3 E= 480,7 x 10^3 N/C e) u= 1/2 E0 E^2 => u= 8,85 x 10^-12 (480 x 10^3)^ u= 1,02 J/m^3 Q19 d= 12,6 cm = 0,126 m U= 8150 V: V/20 u= 1/2 E0 E^2 => E= DV / d u= 1/2 (DV)^2 => u= 1,885 x 10^-12 (8150 / 20)^2 u= 0,074 J/m^3 Q20 Ci= E0 A / d Cf= KE0 A / 2d 1,3 x 10^-12 A /d 2,57E0 A / d xE0 / d KE0 / d 2 x 2,57 x 10^-12 1,3 x 10^12 KE0 E0 K= 3,89
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Lista 3 Q1) E: 8x10^4 V/m d: 0.5mm proton a) ΔV A->B ΔV= -∫ Eo b do ΔV= E0.db ΔV= Eo(0-b) => ΔV= (| ΔV= -8x)) (0.5 .3)6) ====) ΔV= -4x104 ΔV= ΔE (Δ 8'4 1-810\0 (° ) ====> o 1 -08888 - (b) ΔU: =0 proton 16.6x10^-19 9ΔU: ΔU/9 ΔI +866A. A pop (6 ) -0) ΔU 9.=====> 16° 9 => ΔU=6.4 510^ J) Q2) r R1=0.9mm = 0.9x10^-3m R2=2.55mm 2.551x10^-3 | | q4 q3:1mC m: 20mg 209 X 10^-3 | | | ERE+KE+UET Ec= £ 查 (m) CsK.KE+UEDU1=KE+UNa ~ 2-9699(Un)=Uan Un2 | m___m___m\ mv21 U = K90 d ked(Q. o) = Kx9\ | m NO \___p_agebo(\*4-949= ) c=8.999\ | ） q=2\/x10^2|2) 1.9aa=2.955-10 = 1 (...) in V= 2490 mV 2.49 KM) Q3 q1=20mC q2=-20mC q3=10mC d=4cm=0.04m (i) q1 q3 q2 \_|__/=> a) energia potencial no longo d x do eixo x = Vx.q0 a) d V=V1+V2+V3 V1=Kq10mC d V2=K(-20mC) x d V=Kq20mC x x dx9x10 / V23=K(10mC) x 10^-8 x V=U. + 0 6.9 9 U = 0 = V.6 x U=0 36 V=x V=K.q13-V.q01.1 mmh V: K.q13_6m Q4 V=K.qdcosΘ r^2 p .X....p(f) |y || y | z V(K x n^2 + znK) p(x) | K z_eq = 0 Kp x-KRpf\ z n^3 | R^2 = x^2+ -> \ V k00 / (x2^2+z2^2) y + 0+ \n(-> : E(-A): E(r)/_F )-_3 & Belly \ \[ r(s)\ F/() 'xp('/)( /df+r)\ ///="V( gx \ / dyy\ O py+ (x^2+z2^2(3/2) A(p)(3xp^2IdentityP (+z( x16822 ) X Q18 A: 42cm^2 d: 1,3mm DV=625V a) E= EA / d 42 x (10^-4) / 1,3 x 10^-3 E= 8,85x10^-12 x 4,2 x 10^3 => C= 98,59 x 10^-12 F b) C= Q / DV => 98,59 x 10^-12 x 625= Q => Q= 17,86 x 10^-9 c) U= 1/2 C (DV)^2 => U= 98,59 x 10^-12 x 625^2 / 2 U= 5,58 x 10^-5 J d) E= V / d => 625 / 1,3 x 10^-3 E= 480,7 x 10^3 N/C e) u= 1/2 E0 E^2 => u= 8,85 x 10^-12 (480 x 10^3)^ u= 1,02 J/m^3 Q19 d= 12,6 cm = 0,126 m U= 8150 V: V/20 u= 1/2 E0 E^2 => E= DV / d u= 1/2 (DV)^2 => u= 1,885 x 10^-12 (8150 / 20)^2 u= 0,074 J/m^3 Q20 Ci= E0 A / d Cf= KE0 A / 2d 1,3 x 10^-12 A /d 2,57E0 A / d xE0 / d KE0 / d 2 x 2,57 x 10^-12 1,3 x 10^12 KE0 E0 K= 3,89