The alternate rapid reversals of the magnetism in the magnetic field of an electromagnet, when excited by alternating electric currents, sets up eddy currents in every piece of undivided metal within range.  All frames, bobbin tubes, bobbin ends, and the like, must be most carefully slit, otherwise they will overheat.  If a domestic flat iron is placed on the top of the poles of a properly laminated electromagnet, supplied with alternating currents, the flat iron is speedily heated up by the eddy currents that are generated internally within it.  The eddy currents set up by induction in neighboring masses of metal, especially in good conducting metals such as copper, give rise to many curious phenomena.  For example, a copper disk or copper ring placed over the pole of a straight electromagnet so excited is violently repelled.  These remarkable phenomena have been recently investigated by Professor Elihu Thomson, with whose beautiful and elaborate researches we have lately been made conversant in the pages of the technical journals.  He rightly attributes many of the repulsion phenomena to the lag in phase of the alternating currents thus induced in the conducting metal.  The electromagnetic inertia, or self-inductive property of the electric circuit, causes the currents to rise and fall later in time than the electromotive forces by which they are occasioned.  In all such cases the impedance which the circuit offers is made up of two things—­resistance and inductance.  Both these causes tend to diminish the amount of current that flows, and the inductance also tends to delay the flow.

ELECTROMAGNETS FOR QUICKEST ACTION.

I have already mentioned Hughes’ researches on the form of electromagnet best adapted for rapid signaling.  I have also incidentally mentioned the fact that where rapidly varying currents are employed, the strength of the electric current that a given battery can yield is determined not so much by the resistance of the electric circuit as by its electric inertia.  It is not a very easy task to explain precisely what happens to an electric circuit when the current is turned on suddenly.  The current does not suddenly rise to its full value, being retarded by inertia.  The ordinary law of Ohm in its simple form no longer applies; one needs to apply that other law which bears the name of the law of Helmholtz, the use of which is to give us an expression, not for the final value of the current, but for its value at any short time, t, after the current has been turned on.  The strength of the current after a lapse of a short time, t, cannot be calculated by the simple process of taking the electromotive force and dividing it by the resistance, as you would calculate steady currents.

In symbols, Helmholtz’s law is: 

       i_{t} = E/R ( 1 — e^{-(R/L)t} )