THE MAGNETIC FORCE BETWEEN TWO PARALLEL CONDUCTORS Lecture No.12 By. Sajid Hussain Qazi

 When a current-carrying conductor is placed in an external magnetic field B, the magnetic force on the conductor is given by: F = I·(L x B).  Consider two parallel wires of equal length carrying a steady current:  The two wires will exert magnetic forces on each other.  Wire 1 will exert a magnetic force on wire 2; wire 2 will exert a magnetic force on wire 1.

 The wires are separated by distance a and carry currents I 1 and I 2 in the same direction.  Wire 2, carrying current I 2, sets up a magnetic field B 2 at the position of wire 1.  - The direction of the magnetic field B 2 is perpendicular to the wire. - F 1 = F 2 on 1 = I 1 ·(L x B 2 ) - Angle  between L and B 2 is 90.

 F 1 = F 2 on 1 = I 1 ·(L x B 2 ) = I 1 ·L·B 2 ·sin  F 1 = F 2 on 1 = I 1 ·L·B 2  Biot-Savart law for the magnetic field B2:  Substituting:

 Rewriting in terms of the force per unit length:  The direction of F 1 is downward and is determined using the right hand rule (fingers of right hand in direction of current I; palm facing in the direction of B; thumb points down in the direction of F 1 )  The magnetic force that wire 1 exerts on wire 2 (F 1 on 2 ) is equal in magnitude to and opposite in direction to F 1 (F 2 on 1 ).

 Wire 1 and wire 2 will attract each other.  When the currents are in opposite directions, the magnetic forces again equal in magnitude but are opposite in direction and the wires repel each other.  Conclusions: parallel conductors carrying currents in the same direction attract each other; parallel conductors carrying currents in opposite directions repel each other.

Force between two parallel current- carrying straight wires 1. Parallel wires with current flowing in the same direction, attract each other. 2. Parallel wires with current flowing in the opposite direction, repel each other.

 The force between two parallel wires each carrying a current is used to define the ampere (A):  If two long, parallel wires 1 m apart carry the same current I and the force per unit length on each wire is 2 x N/m, then the current is defined to be 1 A.  If I 1 = I 2 = 1 A and a = 1 m, the numerical value of 2 x N/m is obtained from:

 The unit of charge, the coulomb, can be defined in terms of the ampere:  If a conductor carries a steady current of 1 A, then the quantity of charge that flows through a cross-section of the conductor in 1 s is 1 C.