Abstract
We have developed a procedure to determined analytical expressions for the electromagnetic field and impedance of a circular induction coil having an arbitrary orientation in a conductive tube. Initially we express the field of a circular current filament in free space in terms of the global coordinate system referenced to tube axis. This is done by representing the filament field as a single layer potential and forming an integral over the layer using the source coordinates of a static Green’s kernel. A coordinate transform to local source coordinates referenced to the filament axis allows one to determine the coil source function from that of the filament via integration. The effects of induced current in the tube wall on the coil impedance can then be determined for an internal coil. By extension of the present results one can predict the arbitrary orientated coil impedance for an external coil and the impedance variations of a tilted coil due to flaws in tubes.
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