46. The charge dq within a thin shell of thickness dr is ρ A dr where A = 4πr
2
. Thus, with ρ = b/r, we have
q =
dq = 4πb
r
2
r
1
r dr = 2πb
r
2
2
− r
2
1
.
With b = 3.0 µC/m
2
, r
2
= 0.06 m and r
1
= 0.04 m, we obtain q = 0.038 µC.
46. The charge dq within a thin shell of thickness dr is ρ A dr where A = 4πr
2
. Thus, with ρ = b/r, we have
q =
dq = 4πb
r
2
r
1
r dr = 2πb
r
2
2
− r
2
1
.
With b = 3.0 µC/m
2
, r
2
= 0.06 m and r
1
= 0.04 m, we obtain q = 0.038 µC.