Q
2πε0L
ln
(
c
b
)
r < b
Q
2πε0L
ln
(
c
r
)b ≤ r < c
0 r > c
c) V (c)− V (b) = Q
2πε0L
ln
(
c
b
)
a) λ = Q
l
b) σ1 = −Q
2πR1L
;σ2 = Q
2πR2L
c) ~E(r < R0) = ~E(R1 < r < R2) = 0; ~E(R0 < r < R1) = Q
2πρLε0
ρ̂ = ~E(r > R2)
d) σ′1 = −Q
2πR1L
;σ′2 = 0
e) ~E(r > R2) = 0, en el resto de las zonas el campo permanece igual.
f) V = −Q
2πε0L
ln(R1
R0
)
g) C = 2πε0L
ln(
R1
R0
)
h) U = Q2
4πε0L
ln(R1
R0
)i) C′ = C
P 4.14 φ(r) =

Q
8πε0a
+ Q
4πε0a3
(a2 − r2) 0 < r < a
Q
8πε0a
a ≤ r < 2a
Q
4πε0r
r ≥ 2a
P 4.15
a) ~E(z0) =

ρ0δ
ε0
[
1− exp
(
−2a
δ
)]
ẑ z0 > a
−ρ0δ
ε0
[
1− exp
(
−2a
δ
)]
ẑ z0 < −a
b) ~E(z0) =

ρ0δ
ε0
ẑ z0 > a
−ρ0δ
ε0
ẑ z0 < −a
c) V (z) =

V0 −a ≤ z ≤ a
V0 − ρ0δ
ε0
(z − a) z > a
V0 + ρ0δ
ε0
(z + a) z < −a
P 4.16
a) ~E(r) =

0 r < R2
ρ0(r2−R2
2)
2rε0
r̂ R2 ≤ r ≤ R3
ρ0(R2
3−R
2
2)
2rε0
r̂ R3 ≤ r ≤ R4
0 r > R4
σ(r = R1) = 0, σ(r = R4) = − ρ0(R2
3−R
2
2)
2R4
, σ(r = R5) = 0
b) V (R4)− V (R1) = − ρ0
2ε0
(
R2
3−R
2
2
+R2
2 ln
(
R3
R2
)
+ (R2
3 −R2
2) ln
(
R4
R3
))