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Force per Unit Length Between Two Long Parallel Conductors Carrying Current
   
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 μo
 
   
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 10-7Nm-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.  
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