Final answer:
Electric currents in equal and opposite directions cancel each other out due to the properties of vector addition and the interaction of their magnetic fields. The cancellation occurs when considering the vector addition of the magnetic fields produced by the currents, rather than the scalar addition of current itself.
Step-by-step explanation:
Electric currents in equal and opposite directions cancel each other out because of the properties of vector addition. While electric current itself is a scalar quantity, the effects of electric currents can be described using vector addition. When two currents of equal magnitude flow in opposite directions, their magnetic fields interact and partially cancel each other out in certain regions.
For example, when two wires carrying equal currents in opposite directions are placed next to each other, the magnetic field between the wires is augmented, while the magnetic field outside the wires partially cancels. This cancellation occurs because the direction and magnitude of the magnetic fields produced by the currents are taken into account when adding them as vectors.
Although current itself is a scalar, the concept of current density (J) is used to describe the flow of charge with direction. Current density takes into account the local magnitude and direction of charge flow, which varies from point to point. However, when discussing the cancellation of currents, it is the vector addition of the magnetic fields that causes the cancellation, rather than the scalar addition of current itself.