"Where observation is concerned, chance favours only the prepared mind"
Louis Pasteur

• A wire carrying electric current (I) is equivalent to a stream of moving electric charge.  Therefore, it feels a force when placed in an external magnetic field (B).  The magnitude of the force is given by,
  
  
  
  where L is the length of the wire and theta is the angle between the wire and the magnetic field.



• The direction of the force is at right angles to B and I, the sense given by a right hand rule.
  


• Force between two parallel current carrying wires
  
  A long straight wire carrying current produces a magnetic field.  If a second wire is placed in this field it will feel a force of attraction or repulsion to/from the first wire.  For parallel wires carrying currents I₁, I₂ separated by a distance s, the magnitude of the force of attraction/repulsion per unit length between the wires is given by
  
  
  
  Application of right hand rules shows that when the currents are parallel the force between the wires is attractive and when the currents are opposite (anti-parallel) the force is repulsive.
  In the diagram below,  magnetic field lines are blue and the currents are into or out of the plane.






• Definition of the Ampere
  
  "The ampere is that current, which when flowing in two parallel wires 1 metre apart produces a force on each wire of 2 x 10 ^-7 N per metre of length". 
  From above
  
  
  


• The force on current carrying wires is the basis for most electric motors and galvanometers (current measuring device). 

   Supplementary Problems 

"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality"
Albert Einstein


 

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu