A long, straight wire of radius R carries a current distributed uniformly over its cross section. The magnitude of the magnetic field is

Options

A. maximum at the axis of the wire
B. minimum at the axis of the wire
C. maximum at the surface of the wire
D. minimum at the surface of the wire

Answer

B, C

Explanation

Consider the wire as a solid cylinder of radius R.
1. At a point inside : `j=I/(piR^(2))`
Applying ampere's law `impliesint B.dl =mu_(0)IimpliesB=(mu_(0).I)/(piR^(2)) . (pir^(2))/(2piR^(2))`
2. At a point outside
`B.2pir=mu_(0)IimpliesB=(mu_(0)I)/(2pir), B={((m_(0)Ir)/(2piR^(2)), rltR),((mu_(0)I)/(2pir), rgeR):}`