Circular Magnetic Fields: Distribution and Intensity

After reading this section you will be able to do the following:
Explain the distribution and intensity of magnetic fields around conductors
Explain what the skin effect is
As discussed previously, when current is passed through a solid conductor, a magnetic field forms in and around the conductor. The following statements can be made about the distribution and intensity of the magnetic field.

The field strength varies from zero at the center of the component to a maximum at the surface.
The field strength at the surface of the conductor decreases as the radius of the conductor increases when the current strength is held constant. (However, a larger conductor is capable of carrying more current.)
The field strength outside the conductor is directly proportional to the current strength. Inside the conductor, the field strength is dependent on the current strength, magnetic permeability of the material, and if magnetic, the location on the B-H curve.
The field strength outside the conductor decreases with distance from the conductor. Circular Magnetic Fields: Distribution and Intensity
In the images below, the magnetic field strength is graphed versus distance from the center of the conductor. It can be seen that in a nonmagnetic conductor carrying DC, the internal field strength rises from zero at the center to a maximum value at the surface of the conductor. The external field strength decrease with distance from the surface of the conductor. When the conductor is a magnetic material, the field strength within the conductor is much greater than it is in the nonmagnetic conductor. This is due to the permeability of the magnetic material. The external field is exactly the same for the two materials provided the current level and conductor radius are the same.

Circular Magnetic Fields Distribution and Intensity

The magnetic field of a solid conductor carrying current increases linearly with the ubjtc’s radius. Once outside the boundary of the object, the magnetic field begins to decrease exponentially. The magnetic field of a solid magnetic conductor will have a stronger magnetic field than that of a nonmagnetic conductor within the object. Once outside the boundary of the object, the magnetic field drops instantaneously before decreasing exponentially.
The magnetic field distribution in and around a solid conductor of a nonmagnetic material carrying direct current. The magnetic field distribution in and around a solid conductor of a magnetic material carrying direct current.

Instead of increasing linearly, the magnetic field of a magnetic conductor with AC through it increases exponentially until it reaches the radius of the object.
The magnetic field distribution in and around a solid conductor of a magnetic material carrying alternating current.
When the conductor is carrying alternating current, the internal magnetic field strength rises from zero at the center to a maximum at the surface. However, the field is concentrated in a thin layer near the surface of the conductor. This is known as the “skin effect.” The skin effect is evident in the field strength versus distance graph for a magnetic conductor shown to the right. The external field decreases with increasing distance from the surface as it does with DC. It should be remembered that with AC the field is constantly varying in strength and direction. Circular Magnetic Fields: Distribution and Intensity

In a hollow circular conductor there is no magnetic field in the void area. The magnetic field is zero at the inside wall surface and rises until it reaches a maximum at the outside wall surface. As with a solid conductor, when the conductor is a magnetic material, the field strength within the conductor is much greater than it was in the nonmagnetic conductor due to the permeability of the magnetic material. The external field strength decreases with distance from the surface of the conductor. The external field is exactly the same for the two materials provided the current level and conductor radius are the same.

A conductor with a hole in the center and a direct current running through it will have no magnetic field within the whole. At the radius of the hole, the magnetic field will begin to build logarithmically until it reaches the outer radius. Once outside of the outer radius, the magnetic field decreases exponentially. If the object is magnetic, the maximum magnetic field at the border of the outer radius will be mucch greater than the maximum magnetic field strength of a nonmagnetic material. Circular Magnetic Fields: Distribution and Intensity
The magnetic field distribution in and around a hollow conductor of a nonmagnetic material carrying direct current. The magnetic field distribution in and around a hollow conductor of a magnetic material carrying direct current.
A magnetic object with a hole in it that has AC current running through it will produce a sharp magnetic field peak at the outer radius of the object.
The magnetic field distribution in and around a hollow conductor of a magnetic material carrying alternating current.
When AC is passed through a hollow circular conductor, the skin effect concentrates the magnetic field at the outside diameter of the component.

As can be learned from these three field distribution images, the field strength at the inside surface of hollow conductor is very low when a circular magnetic field was established by direct magnetization. Therefore, the direct method of magnetization is not recommended when inspecting the inside diameter wall of a hollow component for shallow defects. The field strength increases rapidly as one moves out (into the material) from the ID, so if the defect has significant depth, it may be detectable.

The magnetic field distribution of a conductor carrying DC inside of a hollow magnetic conductor first increases linearly inside the conductor. Then drops magnetism exponentially between the gap of the object and the surrounding magnet. Then, once inside the magnetic object, the field peaks. once outside of the objects, the magnetic field continues the decrease in strength from where it was in the gap between the objects
The magnetic field distribution in and around a nonmagnetic central conductor carrying DC inside a hollow conductor of a magnetic material .
However, a much better method of magnetizing hollow components for inspection of the ID and OD surfaces is with the use of a central conductor. As can be seen in the field distribution image to the right, when current is passed through a nonmagnetic central conductor (copper bar), the magnetic field produced on the inside diameter surface of a magnetic tube is much greater and the field is still strong enough for defect detection on the OD surface.

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