Figure shown a section through two long thin concentric cylinders of radii a & b with `a gt b`. The cylinders have equal and opposite per unit length `lambda`. Find the electric field at a distance r from the axis for (i) `r lt a` (ii) `a lt r lt b` (iii) `r gt b`

Explanation

[i] `r lt a rArr` Point inside `rArr E=0`
[ii] `a lt r lt b rArr` Point outside the inner and inside the outer so field due to only inner cylinder
hence `E=(2xxlambda)/(r)`
[iii] `r gt b rArr` point outside from both cylinders so the charge per unit length `(lambda)` is zero point `(r gt b) :. E=0`