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Current Loop Radial Reaction Forces


In a companion article the inertial reaction force of a current loop, in response to linear (speed-varying) acceleration in its plane, was discussed. In this article we consider radial (constant speed) acceleration, namely that where a loop’s center goes in a circle at constant speed.

Here again the loop is electrically polarized and has a nonzero E field at its center. Fig. 1 shows a loop at two successive moments. Note that the magnitude of Eo, the electric field at the loop’s center, does not vary in time. But the direction of Eo does vary in time.

Figure 1

Loop, Two Consecutive Instants in Time

It is clear that dE/dt at the loop center points opposite to the center’s velocity at any moment. This induces a circulating B that points toward –z on the loop’s inner leg, and toward +z on the outer leg. There are thus radially outward magnetic forces on the currents in both of these legs. Furthermore, the polarization charges also experience radially outward pointing magnetic forces. Collectively such magnetic forces constitute the loop’s inertial reaction to the external force that makes it go in a circle.

If a loop is only one of many microscopic ones comprising a spinning, disc-shaped, ceramic magnet, then the mass density of the magnet will be greater than another disc, identical in every way except that the matter comprising it is unmagnetized.