Flux Density due to a current flowing in a long straight wire © D Hoult 2008

The field at point p is directed

The field at point p is directed out of the plane of the diagram (“corkscrew rule”)

The magnitude of B at point p depends on

The magnitude of B at point p depends on the current, I

The magnitude of B at point p depends on the current, I the perpendicular distance of p from the wire

The magnitude of B at point p depends on the current, I the perpendicular distance of p from the wire the medium surrounding the wire

Experiments show that B a I and if r is small compared with the length of the wire then

Experiments show that B a I and if r is small compared with the length of the wire then 1 B a r Therefore

Experiments show that B a I and if r is small compared with the length of the wire then 1 B a r Therefore I B = (a constant) r

Because this is a situation having cylindrical symmetry, the factor 2p is included in the equation

Because this is a situation having cylindrical symmetry, the factor 2p is included in the equation 2 p r

Because this is a situation having cylindrical symmetry, the factor 2p is included in the equation 2 p r where µ is the permeability of the medium surrounding the wire

Because this is a situation having cylindrical symmetry, the factor 2p is included in the equation 2 p r where µ is the permeability of the medium surrounding the wire If the medium is a vacuum (or air) the permeability is written as µo

Because this is a situation having cylindrical symmetry, the factor 2p is included in the equation 2 p r where µ is the permeability of the medium surrounding the wire If the medium is a vacuum (or air) the permeability is written as µo The units of µ are

Because this is a situation having cylindrical symmetry, the factor 2p is included in the equation 2 p r where µ is the permeability of the medium surrounding the wire If the medium is a vacuum (or air) the permeability is written as µo The units of µ are T m A-1 =

Because this is a situation having cylindrical symmetry, the factor 2p is included in the equation 2 p r where µ is the permeability of the medium surrounding the wire If the medium is a vacuum (or air) the permeability is written as µo The units of µ are T m A-1 = NA-2

Because this is a situation having cylindrical symmetry, the factor 2p is included in the equation 2 p r where µ is the permeability of the medium surrounding the wire If the medium is a vacuum (or air) the permeability is written as µo The units of µ are T m A-1 = NA-2 1 N A-2 = 1 Henry per meter (H m-1)