Page:Elementary Text-book of Physics (Anthony, 1897).djvu/359

§ 292] before defined in the electrostatic system. Tliat current is defined as the unit current, which will set up the same magnetic field as that due to a magnetic shell of which the edge coincides with the circuit, and the strength is unity.

The unit based upon these definitions is called the electromagnetic unit of current. It is fundamental in the construction of the electromagnetic system of units, in just the same way as the unit of quantity is fundamental in the electrostatic system.

The dimensions of current in the electromagnetic system are the same as those of strength of shell, that is, $$[i] = M^{\frac{1}{2}} L^{\frac{1}{2}} T^{-1}.$$

In practice, another unit of current is used, called the ampere. It contains 10-1 absolute electromagnetic units.

292. Energy of a Current in a Magnetic Field.—It has been shown (§ 289) that the potential at a point in a field due to a current is equal to $$i \Omega,$$ where $$\Omega$$ is the solid angle subtended by the circuit at the point. If a pole of strength $$m$$ be placed at that point, the potential energy of the pole is equal to $$mi \Omega;$$ and since the same amount of work will be done if the circuit be fixed and the pole moved to an infinite distance as is done if the pole be fixed and the circuit removed to an infinite distance, the expression $$mi \Omega$$ also measures the energy of the circuit in the field due to the pole. Now $$4 \pi m$$ is the number of unit tubes which proceed from the pole, and therefore $$m \Omega$$ is the number of unit tubes which pass through the circuit. We may therefore express the energy of the circuit due to the pole by $$i N,$$ where $$N$$ is the number of unit tubes which pass through the circuit. If the circuit be placed in any magnetic field, the forces in the field and the tubes of induction may be considered as due to an assemblage of magnetic poles, to each of which the proposition just stated applies. The energy of the circuit in any magnetic field is therefore given by $$iN,$$ where $$N$$ is the number of tubes of induction due to the field which pass through the circuit. $$N$$ is positive when the tubes of induction of the field pass through the circuit in a direction opposed to that of the tubes of induction of the circuit; and is negative when they pass through in the same direction as that of the tubes of the