Induced voltage is the result of a magnetic flux cutting across a conductor, produced by physical motion of either the magnetic field or the conductor. When the current in a conductor varies in amplitude, however, the variations of current and its associated magnetic field are equivalent to motion of the flux. As the current increases in value, the magnetic field expands outward from the conductor. When the current decreases, the field collapses into the conductor. As the field expands and collapses with changes of current, the flux is effectively in motion. Therefore, a varying current can produce induced voltage without the need for motion of the conductor.
The result of an expanding and collapsing flux field is the same as that of a field in motion.
This moving flux cuts across the conductor that is providing the current, producing induced voltage in the wire itself. Furthermore, any other conductor in the field, whether carrying current or not, also is cut by the varying flux and has induced voltage.
2.4.1 Lenz’s law Definition
Lenz’s law states, “The direction of an induced current is such as to oppose the cause producing it.”
The ‘cause’ of the current may be the motion of a conductor in a magnetic field, or it may be the change of flux through a stationary circuit. In the first case, the direction of the induced current in the moving conductor is such that the direction of the side thrust exerted on the conductor by the magnetic field is opposite in direction to its motion. The motion of the conductor is therefore ‘opposed’.
In the second case, the current sets up a magnetic field of its own, which within the area bounded by the circuit is opposite to the original field if this is increasing, but is in the same direction as the original field if the later is decreasing. Thus it is the change in flux through the circuit (not the flux itself), which is ‘opposed’ by the induced current.
Auto-induction factor
The ability of a conductor to induce voltage in itself when the current changes, is called the auto-inductance or self-inductance or simply the inductance. The symbol for inductance is L and its unit is the Henry. One Henry is the amount of inductance that allows one Volt to be induced when the current changes at the rate of one Ampere per second. The auto-induction factor is given by
The negative sign for E indicates that the polarity of induced voltage is in opposition to the current change, but the polarity can be disregarded in calculating the value of L.
The inductance of a coil increases with the number of turns, diameter of the coil, and the permeability of the core. For a straight air-core coil, the inductance increases as the square of the turns and diameter. Doubling the turns provides four times the inductance, and doubling the diameter provides four times the inductance. If both the number of turns and the diameter are doubled, the inductance is increased by a factor of 16. The inductance also increases directly with the length, i.e. doubling the length provides twice the inductance.
Mutual inductance factor
When the current in an inductor changes, the varying flux can cut across any other inductor nearby, producing induced voltage in both inductors. Consider two coils L1 and L2 placed induces voltage in L1. The two coils have mutual inductance because current in one coil can induce voltage in the other. The mutual inductance of the two coils (M) can be written as
2
The fraction of total flux from one coil linking another coil is the coefficient of coupling. It is denoted by the letter k. The coefficient increases by placing the sensing coil close to the conductor. When probe coils are used, the spacing between the coil and conductor is called lift-off. When encircling or internal coils are used, the coupling is called fill-factor. The coefficient of coupling is increased by placing the coil close to the conductor. A higher value of k, called ‘tight’ coupling, allows better mutual induction. ‘Loose’ coupling, with a low value of k, has the opposite effect.
2.4.2 Induced currents
Induced current in a short-circuit coil
Faraday's law states that whenever a magnetic field cuts a conductor an electrical current will flow in the conductor if a closed path is provided over which current can circulate. The alternating current flowing through the test coil will produce a changing magnetic filed in the coil. If any other coil is placed in the magnetic field of the coil, a current in the second coil will be induced. If the coil is placed very close to the excitation coil then the amount of current induced in the other coil may be the same as that flowing through the excitation coil.
Induced current in a metallic mass
The alternating current flowing through the test coil produces an alternating magnetic field in the coil. When the test coil is brought near to, or placed on the metallic conductor, the magnetic field passes into (cuts) the material and circular (eddy) currents are induced in the material as shown in FIG. 2.17.
FIG. 2.17. Basic eddy current testing equipment.
The current in the conductor (eddy current) will generate a secondary magnetic field, which induces a current in the sensor coil. This mutual inductance causes a change in the impedance of the coil. The impedance signals sensed by the search coil are the measurements of the test specimen. Hence, the eddy current technique uses the effect of electromagnetic fields and induction to characterize physical properties of metallic materials.
Skin effect
Eddy currents induced by a changing magnetic field concentrate near the surface adjacent to the excitation coil. The eddy currents flowing in the test object at any depth produce magnetic fields which oppose the primary field thus reducing net magnetic flux and causing a decrease in current flow as depth increases.
Alternatively, eddy currents near the surface can be viewed as shielding the coil's magnetic field thereby weakening the magnetic field at greater depths and reducing induced currents.
This phenomenon is known as the skin effect.
Field created by eddy current
In a test coil flux is set up by passing the alternating current through it. When this coil is brought close to the conductive sample, eddy currents are induced in the sample. The induced currents have their own magnetic flux associated with them. The direction of the magnetic flux фs associated with the induced currents is such as to oppose the coil’s magnetic flux фp (Lenz’s law) thereby decreasing net magnetic flux. This results in change of coil impedance and voltage drop. FIG. 2.18. illustrates direction of primary and secondary fluxes.
It is the opposition between the primary and secondary (eddy currents) field that provides the basis for extracting information during eddy current testing. It should be noted if sample is ferromagnetic the magnetic flux is strengthened despite opposing eddy current effects. The high permeability of ferromagnetic materials distinguishes them from non-ferromagnetic materials and strongly influences eddy current test parameters.
FIG. 2.18. Field generated by the eddy currents.
Reactance
The net magnetic flux of the coil decreases as its field intercepts a non-magnetic conductive material. This reduces both exciting coil’s inductance and its inductive reactance. The magnitude of this reduction depends on the following:
(a) test materials conductivity (b) test frequency
(c) proximity of the magnetizing coil to the test material.
The test coil reactance in the vicinity of the ferromagnetic material, on the other hand, increases as the highly permeable material is placed in the exciting coil’s field. This happens so as these flux lines which enter the ferromagnetic test part find portion of their path in the material which has far less reluctance than air. The exciting field then includes increased flux densities which are encircled by coil’s windings.
2.5. Factors effecting eddy currents