The Effect of "Neighboring Bodies"

Author: J.B. Hoag

The secondary circuit need not necessarily consist of a coil, condenser, and resistance, as in the cases we have just discussed, but can consist of any metallic, and even a dielectric body, in the neighborhood of the circuit containing the alternating current. A piece of metal placed inside a coil will have small eddy currents induced in it. These currents, in turn, react upon the primary circuit to increase its resistance, i.e., lower its Q, and decrease its inductance and hence increase its resonant frequency. Because of the increased resistance, the generator must supply an additional amount of power (current squared, times resistance). Thus, if we use the symbol R₁¹ for the effective resistance of a circuit (its actual resistance plus that which is " reflected " from the load), we may write

where the term on the left side represents the total power which the source must supply. The first term on the right-hand side of the equation represents the heat developed in the primary circuit, and the second term represents the heat developed in the secondary, or load — be it a circuit or a metallic body or an insulator. Now, this state of affairs may be good or it may be bad. For example, it is " good " when the circuit is used as an induction heater, which consists of a radio frequency generator with a tuned circuit, the coil of which consists of 9. few turns of heavy copper wire. The coil is placed around a body which is to be heated; such, for example, as the metal electrodes sealed inside a vacuum tube during its process of manufacture, or of a human body in which it is desired to develop an " artificial fever." The eddy currents set up in the conductive parts of the body inside the coil cause the body to heat up and, in some cases, to an extent such as to melt it completely.

If an insulator is placed inside the coil, the high frequency electrostatic fields cause the electrical charges in its atoms and molecules to oscillate back and forth about their normal positions. This requires energy which can only come from the primary circuit. This causes the dielectric to heat up, and is spoken of as dielectric loss. That energy should be absorbed from a circuit by a neighboring dielectric is, in general, undesirable. The resistance of the primary circuit is effectively increased by these losses.

We may generalize the concept of resistance by defining it in the following manner:

where the " watts lost " include the heat losses in the circuit itself and in neighboring bodies (as ohmic, eddy current, or dielectric heating); in general, lost in any form whatsoever from the source of power.