Electricity and Magnetism

12–88 Electricity and Magnetism

The physical situation of a very long and narrow system of conductors motivates re-

expression of this result in terms of the effective lineal charge density, λ

0

= Q/L.

Doing so, one obtains

E

r

(R) =

2 k λ

0

R

,

which is identical to the field produced by a thin rod bearing uniformly distributed

charge, cf. Chapter 3.

b < R Outside of the system of conductors, there is no net charge enclosed within

the Gaussian cylinder owing to the equality in magnitude of the [opposite] charges

assigned to each shell. Thus, E

r

(R) 2 π R L = 0, for all R > b, and one must conclude

that the electric field vanishes everywhere throughout this region ...