


Each of the
conductors can be can be considered to be carrying a current which is
flowing through the magnetic field produced by the other current*. 

We will assume that these two conductors are in a vacuum so the permeability
is written as μ_{o} 




In the region of conductor 2, the field produced by the current in conductor
1 is directed out of the plane of the diagram (the corkscrew rule). 

The force on conductor 2 will therefore be directed towards the left
(towards the other conductor), Fleming's left hand rule. 



There will, of course, be an equal and opposite aspect to this force acting
on conductor 1 (Newton's third law of motion). 

This explains why two conductors
with currents flowing in the same sense
attract each other. 



The magnitude of the flux density, B at the position of conductor 2 is 



so the force acting on a length L of conductor 2 is given by 



Therefore, the force per unit length between the two conductors is 





We are considering this situation mainly because it is used to define the
Ampère, as follows: 

1A is that current which, when flowing in
each of two straight, parallel, infinitely long wires, separated by
1m, in a vacuum, produces a force per unit
length of 2×10^{7}Nm^{1} 



Notice that this statement allows us to define what we mean by
1A of current in terms of the fundamental
S.I. units: metres, kilograms and seconds. 



NB: For infinitely long... read, very long compared to the distance
between the wires. 
