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`

Consider a system of two long coaxial cylinders: solid (of radius a ca

1.	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`
Answer» (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`

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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`

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