Consider a system of two long coaxial cylinders: solid (of radius a carrying i current in positive z direction) and hollow (or radius b carrying current i in negative z direction). Find the magnetic field at a point distant r from of the cylinders for
(i) `r le a`
(ii) `a lt r lt b`
(iii) `r gt b`

Explanation

(i) For `r le a`, magnetic field in only due to solid cylinder. Thus it is, `B = (mu_(0)ir)/(2pi a^(2))`
(ii) For `a lt r lt b`, magnetic field is only due to solid cylinder Thus, `B = (mu_(0)i)/(2pir)`
(iii) For `r ge b`, magnetic field is due to both solid and hollow cylinders Thus,
`B_(1) = (mu_(0)i)/(2pir)`, due to solid cylinder
`B_(2) = (mu_(0)i)/(2pir)`, due to hollow cylinder
Also `B_(1) and B_(2)` are in opposite directions
`rArr "Net" B = B_(1) - B_(2) = 0`