Abstract
Magnetic field and eddy currents in a cylinder of finite length are calculated by separation of variables. The magnetic field outside the cylinder or inside the bore of the hollow cylinder and shell is expressed in terms of Bessel functions. Both axial and transverse applied fields are considered for the solid and hollow cylinders. The equations for the vector potential components are transformed in one-dimensional equations along the radial coordinate with the consequent integration by the method of variation of parameters. The equation for the scalar electric potential when required is also integrated analytically. Expressions for the magnetic moment and loss are derived. An alternative analytical solution in terms of scalar magnetic potential is derived for the finite length thin shells. All formulas are validated by the comparison with the solutions by finite–element and finite-difference methods.
Highlights
The paper presents an analytical method of calculation of steady-state magnetic fields and eddy-currents in the cylinder of a finite length placed in the external axial or transverse magnetic field
The main aid of this paper is to derive a general analytical solution in terms of Bessel functions for eddy currents induced in a conductive cylinder by the quasi-static electromagnetic field
We assume that the magnetic field is equal to the applied field at z z z . the current density and electric potential are expanded in the Fourier series over the interval z=[-z0,z0] while the vector potential is fit in the interval z=[z,z ].For the current density and electric scalar potential in the cylinder, we account for the model symmetry jr r sin, r jrl (r)sin l z, l 1 (25)
Summary
The paper presents an analytical method of calculation of steady-state magnetic fields and eddy-currents in the cylinder of a finite length placed in the external axial or transverse magnetic field. It is known that for the infinitely long cylinder the closed form solutions were known in different forms [1,2,3,4]. As it was pointed out by many authors [1,2,5,6] that for the finite length cylinder the general analytical solution had not been available. The main aid of this paper is to derive a general analytical solution in terms of Bessel functions for eddy currents induced in a conductive cylinder by the quasi-static electromagnetic field
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