Ampère, in his communication to the Academy, went on to emphasize the significance of the mechanical effects associated with the newly discovered magnetic phenomena. First of all, recall how Volta had to invoke indirect evidence and the physiological sensations of his own body. Now, however, it is possible to orient a conductor along the north-south axis and a compass above or below the conductor. The degree of deflection is a measure of the amount of current. Ampère gave the name "galvanometer" to such an instrument.

Using his galvanometer, Ampère went on to show that the intensity of the electric current was the same in every portion of the voltaic circuit, including the pile itself. He also showed that if the direction of current in the external circuit is taken by convention to be from the plus to the minus terminal of the pile, the current within the pile is in the opposite direction-from minus to plus. This, of course, strongly reinforced the concepts of circuit and of continuity of flow of charge that were embedded in the initial working hypotheses. Furthermore, Ampère gave a statement of what was qualitatively known to most "electricians" of the time, but remained to be quantitatively formulated by Georg Simon Ohm some years later, namely that a frictional machine produces much less current than a voltaic pile, "because the quantity of electricity produced by a frictional machine remains the same in a given time regardless of the conducting power of the rest of the circuit, whereas that which the pile sets in motion during a given time increases indefinitely as we join the two extremities by a better conductor."

The galvanometer, as already used by Oersted and christened by Ampère, quickly became a vital tool in electrical research. Faraday used just such a device in his discovery of electrical induction, and Ohm depended on it for his study of the conducting power of electric circuits. As time went by, the delicacy of the magnetic-needle galvanometer was tremendously increased, but variations of the effect with distance from, and orientation relative to, the conductor remained a fundamental limitation on accuracy and reproducibility of quantitative measurement. Ultimately this instrument gave way to a still more sensitive and reproducible device-one in which a moving coil, itself part of the electric circuit and carrying the current being measured, rotates in the field of a fixed magnet against the restoring torque of a coil spring.

Our present methods of measuring electric current and defining its unit evolved from Ampère's experiments. Let's see how. It is tempting to assume a direct proportionality or linear relationship between the intensity of the current and its mechanical effects, such as the torque on the magnetic galvanometer needle. This assumption is already implicit in the early observations of Oersted and Ampère. We have a prior intuitive notion of electric current in terms of quantity of charge and the rate at which it moves past a point in a conductor. It is entirely possible, in principle, that current, visualized in this way, is not linearly related to the torque on the compass needle. If this were the case, and if we followed Ampère's implied suggestion and defined current in terms of torque on the galvanometer, we would eventually run into inconsistencies and contradictions between the two points of view. That is, we would have defined two entirely different "currents," and would be confusing the issue by using the same name for different operational concepts.

Accumulated experience, however, indicates that the linearity assumption is valid and that the concepts are not contradictory. We shall see all these ideas flow together in subsequent discussions, but for the time being we can reinforce the view with a simple experiment. When two loops of the wire are so arranged as to carry current in the same direction, twice as much current must flow past a point of observation per unit time as flows past a point of observation near a single wire. If the magnetic effect is indeed proportional to the rate of flow of charge (that is, if a simple superposition law is obeyed), we should observe twice the torque at the double wire as at the single ones. If the wire were formed into three loops, we should observe three times the torque, etc. Similarly, in regions where the currents are equal and opposite, the net transport of charge past a point of observation should be zero, and we would expect the magnetic effect near such a region to be zero. All of which are confirmed by observation [demo].

In a device known as a current balance, the force between two current-carrying coils of wire can be weighed directly by balancing the system in the absence of current and noting the additional weight necessary to rebalance it when current flows. If the coils have fairly large radii, they interact with each other very nearly like straight parallel wires.

The following quantitative effects and relations are observed in experiments with a current balance:

1. At a fixed separation d between the loops, the total force between them increases if either loop is connected to a larger voltaic pile; that is, if the current in either loop is increased. If the current in each wire is kept fixed and one of them is coiled so as to make two loops, the observed force is doubled. If each wire is coiled into two loops, the observed force is four times that which obtains when the wires form single loops carrying the same current. Denoting the currents in the wires by I₁ and I₂, respectively, we are led to the conclusion that the total force between parallel wires is proportional to the product I₁I₂ of the two currents.
2. For fixed current, the force between the wires is found to be inversely proportional to the separation d.
3. For fixed current and separation, the total force between the wires is found to vary with the length L over which the conductors are essentially parallel to each other. Measurements show that the total force F is directly proportional to L, and the ratio F/L then denotes force per unit length of wire.

Summarizing in one algebraic equation the empirical results just described, we have F (I₁I₂)/(d)L; (F)/(L) (I₁I₂)/(d); (F)/(L) = k_M(I₁I₂)/(d).

If the two wires are connected in series with each other to the same battery, the two currents are identical, and these equations take the form

(F)/(L) (I²)/(d); (F)/(L) = k_M(I²)/(d).

The subscript M attached to the proportionality constant is there to remind us that this constant is associated with a magnetic interaction.

The current balance thus provides a simple and direct way of relating an electric current to a measurable mechanical force. In our modern system of MKS units, we take advantage of this fact to define the unit in which current is to be expressed. This unit is called the ampere, and is defined as: that unvarying current which, if present in each of two parallel conductors of infinite length one meter apart, causes each conductor to experience (in vacuum) a force of exactly 2 ×10^-7 newton per meter of length. Given this definition, we can establish the value of any particular current by measuring with a current balance the force between wires of known length and separation.

Having assigned k_M a specific numerical value (in vacuum) and thus established a unit of current and thereby the calibration of current meters, it then becomes possible, in principle, to use a current balance to determine the force between conductors immersed in air, oil, or other media under conditions of known current. It is found experimentally that the force depends on the medium as well as on I and d, and that therefore k_M must be an intrinsic property of a given medium, just as k_E in Coulomb's law is also found to be such an intrinsic property. Actually, measurements of this kind are made indirectly, with devices far more sensitive than a current balance, but the principle is unaltered.

Information provided by: http://www.arts.richmond.edu