III. MATERIALES Y MÉTODOS
3.3 CUENCAS HIDROGRÁFICAS
Before discussing the principles of eddy current testing, it seems appropriate to briefly discuss the concept of magnetism and electromagnetism that serve as the foundation for this study. In the period from 1775 to 1900, scientific experimenters Andre Marie Ampere, Françios Arago, Charles Augustin coulomb, Michael Faraday, Lord William Thomson Kelvin, James Clerk Maxwell and Hans Christian Oersted had investigated and
cataloged most of what is known about magnetism and electromagnetism. Arago discovered that the oscillation of a magnet was rapidly damped when a nonmagnetic conductor disk was placed near the magnet. He also observed that by rotating the disk, the magnet was attracted to the disk. In effect, Arago had introduced a varying magnetic field into the metallic disk causing eddy currents to flow in the disk. This produced a secondary magnetic field in the disk that affected the magnet. Arago's simple model is a basis for many automobile speedometers used today. This experiment can be modeled as shown in Figure 1.1.
Charlie Chong/ Fion Zhang
Arago’s Disk Experiment
Arago discovered that the oscillation of a magnet was rapidly damped when a nonmagnetic conducting disk was placed near the magnet. He also observed that by rotating the disk, the magnet was attracted to the disk. In effect, Arago had introduced a varying magnetic field into the metallic disk causing eddy currents to flow in the disk. This produced a secondary magnetic field in the disk that affected the magnet. Arago's simple model is a basis for many automobile speedometers used today.
Charlie Chong/ Fion Zhang
Oersted discovered the presence of a magnetic field around a current carrying conductor and observed magnetic field developed in a perpendicular plane to the direction of current flow in a wire. Ampere observed that equal and opposite currents flowing in adjacent conductors cancelled this magnetic effect. Ampere's observation is used in differential coil applications and to
manufacture non inductive precision resistor. Faraday's first experiments investigated induced currents by the relative motion of magnet and a coil (Figure 1.2). Faraday's major contribution was the discovery of electromagnetic induction. His work can be summarized by the example shown in Figure 1.3.
A coil "A" is connected to a battery through a switch, "S", A second coil, B, connected to a voltmeter is near by. When switch S is closed it produces a current in coil A in the direction shown (a). A momentary current is also induced in coil in direction (b) opposite to the current flow in coil A. If S is now opened, a momentary current will appear in coil B having the direction of (c). In each case current flows in coil B only while the current in coil A is changing.
Charlie Chong/ Fion Zhang
Figure 1.3: Induced current electromagnetic technique
A coil "A" is connected to a battery through a switch, "S", A second coil, B, connected to a voltmeter is near by. When switch S is closed it produces a current in coil A in the direction shown (a). A momentary current is also induced in coil in direction (b) opposite to the current flow in coil A. If S is now opened, a momentary current will appear in coil B having the direction of (c). In each case current flows in coil B only while the current in coil A is changing.
Electromagnetic induction
is the production of an electromotive force across a conductor when it is exposed to a varying magnetic field. It is described mathematically by Faraday's law of induction, named after Michael Faraday who is generally credited with the discovery of induction in 1831.Electromagnetic induction was first discovered by Michael Faraday, who made his discovery public in 1831. It was discovered independently by Joseph Henry in 1832.
In Faraday's first experimental demonstration (August 29, 1831), he wrapped two wires around opposite sides of an iron ring or "torus" (an arrangement similar to a modern toroidal transformer). Based on his assessment of recently discovered properties of electromagnets, he expected that when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. He plugged one wire into a galvanometer, and watched it as he connected the other wire to a battery. Indeed, he saw a transient current (which he called a "wave of electricity") when he connected the wire to the battery, and another when he disconnected it. This induction was due to the change in magnetic flux that occurred when the battery was connected and disconnected. Within two months, Faraday found several other manifestations of electromagnetic induction. For example, he saw transient currents when he quickly slid a bar magnet in and out of a coil of wires, and he generated a steady (DC) current by rotating a copper disk near the bar magnet with a sliding electrical lead ("Faraday's disk"). Faraday explained electromagnetic induction using a concept he called lines of force. However, scientists at the time widely rejected his theoretical ideas, mainly because they were not formulated mathematically. An exception was Maxwell, who used Faraday's ideas as the basis of his quantitative electromagnetic theory. In Maxwell's model, the time varying aspect of
electromagnetic induction is expressed as a differential equation which Oliver Heaviside referred to as Faraday's law even though it is slightly different from Faraday's original formulation and does not describe motional EMF. Heaviside's version (see Maxwell– Faraday equation below) is the form recognized today in the group of equations known as Maxwell's equations.
Heinrich Lenz formulated the law named after him in 1834, to describe the "flux through the circuit". Lenz's law gives the direction of the induced EMF and current resulting from electromagnetic induction (elaborated upon in the examples below).
Faraday's Law - Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating the coil
relative to the magnet, etc. Faraday's law is a fundamental relationship which comes from Maxwell's equations. It serves as a summary of the ways a
voltage (or emf) may be generated by a changing magnetic environment. The induced emf in a coil is equal to the negative of the rate of change of
magnetic flux times the number of turns in the coil. It involves the interaction of charge with magnetic field.
Charlie Chong/ Fion Zhang
The law of physics describing the process of electromagnetic induction is known as Faraday's law of induction and the most widespread version of this law states that the induced electromotive force in any closed circuit is equal to the rate of change of the magnetic flux enclosed by the circuit. Or mathematically,
ε = dфB/ dt
where ε (epsilon) is the electromotive force (EMF) and ΦB (Φ= BA) is the magnetic flux. The direction of the electromotive force is given by Lenz's law. This version of Faraday's law strictly holds only when the closed circuit is a loop of infinitely thin wire, and is invalid in some other circumstances. A different version, the Maxwell–Faraday equation (discussed below), is valid in all circumstances. For a tightly wound coil of wire, composed of N identical turns, each with the same magnetic flux going through them, the resulting EMF is given by
ε = -N dфB/ dt
Faraday's law of induction makes use of the magnetic flux ΦB through a hypothetical surface Σ whose
boundary is a wire loop. Since the wire loop may be moving, we write Σ(t) for the surface. The magnetic flux is defined by a surface integral:
фB =
∫
Σ(t) B(r,t)∙dAwhere dA is an element of surface area of the moving surface Σ(t), B is the magnetic field, and B·dA is a vector dot product (the infinitesimal amount of magnetic flux). In more visual terms, the magnetic flux through the wire loop is proportional to the number of magnetic flux lines that pass through the loop.