By Herbert H. Woodson

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**Extra resources for Electromechanical Dynamics - Fields Forces and Motion**

**Sample text**

The system consists of an electromagnet made of in qfin, il At d1%a1xn * l b+1 +t material with an air gap of length wand excited through the N-turn winding by a constantcurrent source I which can be turned on or off by the switch S. In the air gap is a slab of nonmagnetizable (/z = ~ 0) material of the dimen- sions shown and with constant electrical Bo conductivity a. We assume that the switch S is initially closed so that there is no current through the winding and no flux in the magnet. At t = 0 switch S is opened, and we wish to determine ,mhtnr 0t er t Fig.

Points of constant phase on the current sheet move to the right with the velocity w/k, where both w and k are given. This example has attributes that make it possible to demonstrate the basic mechanism responsible for several practical magnetic induction-type interactions. As we shall see, currents are induced in the conducting material. Te K- = K cos (uot - kz) 1. Fig. 18 A slab of conducting material moves in the z-direction with velocity V. Just below the slab sinusoidally distributed windings are driven by a traveling wave of surface current density which has the phase velocity w/k to the right.

5 has odd symmetry about z = d/2. Note that the onedimensional solution implies perfectly conducting end plates on the slab to provide a return path for the currents. It should be clear from a study of Figs. 5 that if we are interested in electromagnetic phenomena that occur outside the slab and that have characteristic times much shorter than the diffusion time 7 we can approximate the properties of the slab by saying that a -- co. In this approximation the flux is excluded from the interior of the slab and currents flow on the surfaces.

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