Campos magneticos

William Andrés Lievano Campos 20082007001

1) ra=5mm rb=12mm e1=1.5 e2=9 σ1=2*10-6 σ2=5*10-9 V1=50 V0=20

a) -C1 /r + C2 =20 b) -C1 /r + C2 =50-C1 /(0.005) + C2 =20 -C1 /(0.012) + C2 =50

Resolvemos el sistema de ecuaciones.

C1 = 0.25 C2 = 71.45

V= -0.25 /r + 71.42
E=-0.25/r2

I= ∫EσdsI1= ∫0.25/r2 r2 senθ dθ dϕ cancelamos los r2

I=0.025σ [∫senθ dθ] + [∫dϕ] 0<dθ> π0 <dϕ >2π

I= 0.025(2*10-6 ) (2 π)
I= 3.14*10-7

I2= ∫Eσds I1= ∫0.25/r2 α r2 senθ dθ dϕ cancelamos los r2

I=0.025σ[∫senθ dθ] + [∫dϕ] 0<dθ> π 0 <dϕ >2π

I= 0.025(5*10-9 ) (2 π)
I2= 7.85*10-9

Q= ∫E0 Er1 E ds Q=∫E0 Er10.25/r2 r2 senθ dθ dϕ cancelamos los r2

Q= 8.84*10 -12 (1.5)0.25 [[∫senθ dθ] + [∫dϕ] 0<dθ> π 0 <dϕ >2πQ=3.15*10-12 (2 π)
Q=2.082*10-11

Q2= ∫E0 Er1 E ds Q=∫E0 Er1 0.25/r2 r2 senθ dθ dϕ cancelamos los r2

Q2= 8.84*10 -12 (9)0.25 [[∫senθ dθ] + [∫dϕ]0<dθ> π 0 <dϕ >2π
Q2=1.98*10-12 (2 π)
Q=1.24*10-11

V= ∫Edl V1=∫ 0.25/r2 dr0.012<r>0.005

V=0.025[-200-(83.33)]
V=29.16

R=V/I
R1= 29.16/3.14*10-7
R1 =92866242.04

R=V/I
R1= 29.16/ 7.85*10-9
R1 =3714649682

C= Q/V
C1 =2.082*10-11 / 29.16

C1 = 7.13*10-13C= Q/V
C2 = 1.24*10-11/ 29.16

C2 = 4.25*10-13

2) R=4cm ρv=10*10-6

r<R

∫D ds= ∫ ρvdv la integral de Dds es...