Magnetic Force Between Two Parallel Currents

When currents flow in the same direction, the magnetic field created by each conductor exerts an attractive force on the other. If the current direction is reversed in either conductor, the force becomes repulsive. The force direction is determined by applying the right-hand rule to the cross-product of the length vector and magnetic field.

The force exerted by the magnetic field of the first conductor on a finite length of the second conductor equals the current in the second conductor multiplied by the vector product of the length vector and the magnetic field. This cross-product relationship yields the force magnitude and direction between the conductors.

One Ampere is defined as the current in each of two parallel, infinitely long conductors separated by one meter in empty space that produces a force of exactly 1 Newton per meter between them. This definition uses the measurable force between parallel conductors as a fundamental standard for current measurement.

The pinch effect occurs when the attractive magnetic force between parallel currents squeezes current into a smaller tube. It appears in electric arcs and plasmas where charges move parallel to one another. In circuit breakers and solar plasma, this effect can concentrate arcs, burn holes in equipment, or shape solar flares and jets of ionized material.

The right-hand rule for the cross-product determines force direction by pointing your fingers along the length vector, curling them toward the magnetic field direction, and extending your thumb perpendicular to both. This thumb direction indicates the force on the conductor carrying current in the magnetic field.

The magnetic attraction between parallel currents is apparent when the overall charge density is zero. In this condition, Coulomb repulsion does not overwhelm the magnetic attraction. When charge density is not zero, electrostatic repulsion becomes dominant and masks the magnetic force effects.

Force per unit length expresses the magnetic force between very long parallel conductors as force divided by conductor length. This normalized measurement simplifies calculations and comparisons, forming the basis for defining the Ampere unit and analyzing effects like the pinch effect in extended current-carrying systems.