Basic electromagnetic theory states that a moving charge will produce a magnetic field. If the charge is confined to conduction current, such as the current through a straight wire, then a magnetic field will rise around the wire in the circular direction governed by the algebraic vector curl within Ampere's Law. If you were to imagine a wire coming straight out of the screen, then the magnetic field present on the screen will curl counterclockwise around the wire. A current flowing into the screen will produce a clockwise curl. Armed with this knowledge, it is possible to bend the wire in such a way that concentrates the magnetic field.
The figures below represent a simulation of the density of the magnetic fields created by a varying number of wire loops (in air) through the use of FEMM analysis software (the outer circular boundary is estimated to be infinity). Each figure is an axisymmetric cross-section of a three-dimensional model and the greatest densities approach a red color.
Take for example a single closed loop of wire (first figure) carrying some current. The sum of all of the magnetic flux lines around the inside of the loop will result in a vector pointing along the axis of the loop. The next figure shows the flux lines and magnetic field of three loops of wire carrying an even distribution of the same current. As the number of loops increase, the maximum magnetic field density becomes more evenly distributed throughout the center. When the number of loops becomes large and they are all closely spaced, we can make an approximation and disregard the effects of their circular cross-section. By doing so we can also disregard the discrepancy in symmetry of a single wire wrapped into a coil. The last figure shows this approximation as a solid hollow cylinder conducting a current equal to the initial current times the number of turns.
The result is something similar to a bar magnet with north and south poles. According to Gauss' Law of Magnetism, every flux line forms a closed path. You can see that this is true (if you imagine the the continuation of the lines beyond the graph's boundary).
To continue: a change in magnetic field will induce a current in a conductive object in that magnetic field. Conductive objects, such as metals, do not have as strong an attachment to valence electrons as do plastics or high-dielectric materials. Therefore it is safe to say that if the core of a solenoid is a conductive material, a current will arise in a direction opposing the magnetic field that induced it. This comes directly from the conservation of energy. We can expand this and conclude that the current in the conductor flows in the direction to oppose the change in current of the solenoid. These "induced" currents are called eddy currents.
Eddy currents flow in circular patterns on the surface of conductive objects within a changing magnetic field. Their current density decreases with depth into the conductor. The rightmost figure is an axisymmetric simulation of a solenoid laying on top of a block of aluminum. Current through the solenoid oscillates at 1kHz. Notice how the maximum density is closest to the surface, due to the skin effect.
An induction heater uses eddy currents to heat objects very quickly to precise temperatures with out any physical contact. They are commonly found in the manufacturing and metal-working industry, as well in physical research labs. The idea behind them is to create as large a change in current as quickly as possible. The eddy currents will flow through what ever resistance the target object has to offer. Though usually small, the total power dissipated by the object will be equal to the resistance times the square of the current. When the eddy currents are large, the object heats up very fast.
Above is a photo of a makeshift induction heater using a an MOT (microwave transformer), a diode, and a high voltage microwave capacitor. The idea here is to charge the 2000WVAC 0.94uF capacitor and discharge the current through a spark gap into an inductive load. The load will be referred to as the work coil. In the photo, the work coil is wrapped about 15 times around a ferrite core (for magnetic response purposes). The spark gap is nothing more then two pieces of aluminum scrap spaced less than 1mm apart, which will provide a huge change in current.. The source of electricity includes a power strip with a built-in circuit breaker rated for 15A. This is for safety reasons, plus I did not want have to get up and reset the main breaker every time it tripped.
The capacitor instantly charges to the full rectified voltage of the transformer output, which is around 2kVDC, and was free to discharge across the spark gap 60 times per second (60Hz is the American standard power line frequency). The discharge is loud and produces a bright white flash, as seen in the picture.
The wall drew enough power to trip the circuit breaker every 5 to 6 seconds, and I had to wait a moment while it resetted itself. After a few runs, the work coil became critically hot since I used cheap 22 gauge wire. The black insulation started smoking and melting off of the wires, and eventually burst into flames. Somewhere in the solenoid two adjacent coils melted together and shorted the whole thing out. The ferrite core became quite hot and proved that the circuit supplied a good amount of power.
Now for the real test: I went out to Radioshack and bought some magnetic wire. The insulation is enamel (not rubbery plastic) so I was less concerned about making a mess. However, the wire was much thinner and will heat up faster which is undesired. I rolled up a piece of paper into a tube and wrapped it with about 250 turns. A larger number of turns will increase the magnetic field, but it will also increase the inductance, which in turn decreases the change in current. There is an optimization point somewhere in between, but I wasn't about to figure it out.
The core object was changed to a steel finishing nail (with a higher conductivity) that somehow made its way into my toolbox. I put the nail in the core and turned on the power.
The spark gap was not as intense as it was with the ferrite core because of the increase in inductance. It only took a second for the center of the nail to start glowing red hot.
The circuit breaker tripped just as the paper started to smoke. The left picture shows what the nail looked like after it had been heated. It is clear where the eddy currents circulated around the surface within the work coil's core and worked the nail into a black color. The work coil itself became hot due to ohmic heating.
This is an simulation demonstrating the formation of eddy currents. The upper block is the cross-section of the coil, and the lower block is the nail. The model is axisymmetric, so imagine everything rotated evenly around the zero (blue) axis.
As the magnetic field changes, it induces a current in the nail. The current density is represented by the change of colors with red being the most intense. Notice how the current only rotates around the nail on the surface, due to the skin effect.
I continued to power the circuit after the nail had been removed until the work coil became so hot that the enamel burned/melted off and shorted at the lead points. The wire was so thin that it effectively turned into a heating element. You can see the picture of the glowing wire at the right. After a few more seconds, the wire burned out with a loud snap.
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