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

4. The field at point p is directed

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

7. The magnitude of B at point p depends on

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

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

10. 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

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

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

13. 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

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

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

16. 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

17. 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

18. 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

19. 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 =

20. 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

21. 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)