Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/173

are here directed towards the north. The direction of the force acting on the second current is to be determined by turning the handle of a right-handed screw from the nadir, the direction of the current, to the north, the direction of the magnetic induction. The screw will then move towards the east, that is, the force acting on the second current is directed towards the first current, or, in general, since the phenomenon depends only on the relative position of the currents, two parallel currents in the same direction attract each other.

In the same way we may shew that two parallel currents in opposite directions repel one another.

495.] The intensity of the magnetic induction at a distance $r$ from a straight current of strength $i$ is, as we have shewn in Art. 479,

$2{\frac {i}{r}}.$

Hence, a portion of a second conductor parallel to the first, and carrying a current $i'$ in the same direction, will be attracted towards the first with a force

$F=2ii'{\frac {a}{r}},$

where $a$ is the length of the portion considered, and $r$ is its distance from the first conductor.

Since the ratio of $a$ to $r$ is a numerical quantity independent of the absolute value of either of these lines, the product of two currents measured in the electromagnetic system must be of the dimensions of a force, hence the dimensions of the unit current are

$[i]=[F^{\frac {1}{2}}]=[M^{\frac {1}{2}}L^{\frac {1}{2}}T^{-1}].$

496.] Another method of determining the direction of the force which acts on a current is to consider the relation of the magnetic action of the current to that of other currents and magnets.

If on one side of the wire which carries the current the magnetic action due to the current is in the same or nearly the same direction as that due to other currents, then, on the other side of the wire, these forces will be in opposite or nearly opposite directions, and the force acting on the wire will be from the side on which the forces strengthen each other to the side on which they oppose each other.

Thus, if a descending current is placed in a field of magnetic force directed towards the north, its magnetic action will be to the north on the west side, and to the south on the east side. Hence the forces strengthen each other on the west side and oppose each