A wire of radius 0.7 cm carries a current of 150 A that is uniformly distributed

Question

A wire of radius 0.7 cm carries a current of 150 A that is uniformly distributed over its cross-sectional area. The permeability of free space is 4 × 107 T · m/A.

a) 107 T · m/A. Find the magnetic field at a distance of 0.3 cm from the center of the wire. Answer in units of T.

b) Find the magnetic field at the surface of the wire

c) Find the magnetic field at a point outside the wire 0.3 cm from the surface of the wire. Answer in units of T.

Could someone walk me through this step by step? I am particularly confused about part A. I use ampere's law for a point at radius r within the radius R of the wire and get .0018, but my homework site says this is wrong. I must be missing something really basic.

Explanation / Answer

when r<R , the magnetic field of a long wire is defined like

B = ( 0 i r ) / ( 2 R2 )

B = ( 4x10-7 T.m/A * 150 A * 0.003 m ) / ( 2 ( 0.007 m )2 )

B = 0.0018 T

b) at the surface

B = ( 0 i r ) / ( 2 R2 )

B = ( 4x10-7 T.m/A * 150 A * 0.007 m ) / ( 2 ( 0.007 m )2 )

B = 0.0043 T

c) when r>R , the magnetic field of a long wire is defined like

B = ( 0 i ) / ( 2 r )

B = ( 4x10-7 T.m/A * 150 A ) / ( 2 0.01 m )

B = 0.003 T

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