Page 128 - Maxwell House

108 Chapter 2

formed there. By Faraday’s Law (see the equation (1.42)) the derivative Φ () of time-
⁄

varying magnetic flux is negative and therefore the induced
electromotive force ℰ() > 0 drives free electrons in pipe
walls and kicks off the top eddy current (top blue circles),
35
as Figure 2.10.2 depicts. Since the magnetic fields created
by this top eddy current and the falling magnet are opposite
the attractive upward force is exerted that opposes to gravity
and thus slows down the magnet fall. Exactly the same way
the induced
Figure 2.10.3 Rotating disk bottom eddy Electromagnet
in magnetic field current in
Figure
2.10.2 produces the repulsive and upward
directed force that brakes the fall even more. By
mechanics laws, the acceleration of the magnet
steadily decreases until it reaches zero. Finally,
as this equilibrium is reached the magnet
continues its fall with constant velocity called
terminal. Such magnetic braking force of eddy
current eventually gets higher if the magnet
becomes stronger, pipe walls thicker and their
electric conductivity higher.
Metal Drum
The similar eddy-current braking effect will take
place if we put a spinning conductive disk Figure 2.10.4 Eddy-current brakes
between the poles of a strong permanent magnet
as shown in Figure 2.10.3 . The magnetic field of induced by a magnet in disk eddy current
36
creates the damping torque force that opposes to the force rotating the disk. Figure 2.10.4
37
illustrates the eddy-current brakes for the train where the metal drums are attached to the train
wheelset axle. When the brakes need to be activated, the powerful electromagnets switch on
and apply a strong magnetic field across the drums. Then the induced eddy currents in the drums
initiate the torque force that opposes the motion of the wheel reducing by that the train speed.
Such brakes are quiet, frictionless, and wear-free because they make no physical contact with
any friction pads and require little or no maintenance. They produce no smell or pollution
(unlike traditional friction brakes, which can release toxic chemicals into the environment).
2.10.5 Eddy Current in Power Transformer Core

We have mentioned above that eddy currents in power transformer cores are undesirable and
represent lost electric power. The simplest power transformer schematic is given in Figure
2.10.5 and comprises the ferromagnetic (typically steel) core and two solenoids wrapped around
it. According to Faraday’s law (1.42) the time-varying voltage ℰ () applied to the primary
1
solenoid consisting of turns produces the electric current in the wires and magnetic flux
1
1
(magenta line in Figure 2.10.5) circulating inside the core.

35 Public Domain Image, source: http://sciphile.org/lessons/slow-motion-magnets
36 Public Domain Image, source: https://www.comsol.com/model/magnetic-brake-2014
37 Public Domain Image, source:
https://ja.wikipedia.org/wiki/%E3%83%A1%E3%82%A4%E3%83%B3%E3%83%9A%E3%83%BC%
E3%82%B8