The Magnetic Force Between Two Parallel Conductors AP Physics C Montwood High School R. Casao

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.