1) An inductive coil can be examined by use of computational approaches. For computing the inductance, we need to consider the surrounding air and the magnetic core materials together. In this technique, the air domain around is discretized by meshes called as finite volumes. The figure on right shows this mesh structure around the inductive coil. We need to calculate the magnetic flux across one of the control volumes which is given by the following figure. The vector field (magnetic field) around this finite volume is given by, F = (xi + cos y)i + (ešinx + 5yx)j + (ln xy + 8xz)k Normally “flux" across the surface of closed volumes can be calculated by “surface integrals". However, if such an integral gives you trouble, you can think about using one of the following theorems; • Stokes' theorem The control volume for the magnetic flux calculation in an air domain including a coil surrounding a magnetic core. • Divergence theorem of Gauss a) If you intend to use one of the theorems, indicate clearly which theorem you want to use. b) Calculate the magnetic flux across the given control volume. 2.

1) An inductive coil can be examined by use of computational approaches. For computing the inductance, we need to consider the surrounding air and the magnetic core materials together. In this technique, the air domain around is discretized by meshes called as finite volumes. The figure on right shows this mesh structure around the inductive coil. We need to calculate the magnetic flux across one of the control volumes which is given by the following figure. The vector field (magnetic field) around this finite volume is given by, F = (xi + cos y)i + (ešinx + 5yx)j + (ln xy + 8xz)k Normally “flux" across the surface of closed volumes can be calculated by “surface integrals". However, if such an integral gives you trouble, you can think about using one of the following theorems; • Stokes' theorem The control volume for the magnetic flux calculation in an air domain including a coil surrounding a magnetic core. • Divergence theorem of Gauss a) If you intend to use one of the theorems, indicate clearly which theorem you want to use. b) Calculate the magnetic flux across the given control volume. 2.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

1) An inductive coil can be examined by use of computational
approaches. For computing the inductance, we need to consider
the surrounding air and the magnetic core materials together. In
this technique, the air domain around is discretized by meshes
called as finite volumes. The figure on right shows this mesh
structure around the inductive coil. We need to calculate the
magnetic flux across one of the control volumes which is given by
the following figure. The vector field (magnetic field) around this
finite volume is given by,
F = (xi + cos y)i + (ešinx + 5yx)j + (ln xy + 8xz)k
Normally “flux" across the surface of closed volumes
can be calculated by “surface integrals". However, if
such an integral gives you trouble, you can think about
using one of the following theorems;
• Stokes' theorem
The control volume for the magnetic flux calculation in an
air domain including a coil surrounding a magnetic core.
• Divergence theorem of Gauss
a) If you intend to use one of the theorems, indicate clearly which theorem you want to use.
b) Calculate the magnetic flux across the given control volume.
2.

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