Symbolic Analysis of Magnetic Field with Symbolic Analysis of Magnetic Field with the Biot-Savart-Laplace Method

Daniel Ioan and Irina Munteanu

11  Proposed projects

11.1  Problem 1

Determine the expression of magnetic field components, produced in the origin by a current-carrying segment of conductor, whose ends are in the points P1 (x1, y1, z1) and P2(x2, y2, z2). Starting from this expression, determine, by translation, the field in an arbitrary point P(x, y, z). Generate a function in C programming language, able to compute the field components.

11.2  Problem 2

Determine the expression of magnetic field components, produced by an arbitrary triangle with vertices P1, P2, P3, carrying the current i. Plot the variation of the field magnitude in the plane of the triangle.

11.3  Problem 3

Determine the expression of magnetic field components, produced by a rectangular filamentary conductor carrying the current i. Plot the variation of the field magnitude along a symmetry axis normal to the rectangle's plane. Determine the expression of the magnetic field produced by a square of area A, when A tends to zero while the product Ai remains constant. Plot the magnetic field lines in this case.

11.4  Problem 4

Generate a procedure for computing the magnetic field produced by an arbitrary polygonal line with given vertices P1, P2, ... Pn, carrying the current i. Plot the polygonal line and the field vectors.

11.5  Problem 5

Generate a procedure for computing the magnetic field produced by filamentary conductor carrying the current i, which follows an arbitrary curve described by the parametric functions x(t), y(t), z(t), cu t0 < t < t1.

11.6  Problem 6

Determine the magnetic field and the vector potential produced, outside its axis, by a circular filamentary conductor carrying the current i. Plot the vectors of the magnetic field and of the vector potential, at great distance from the conductor, using an approximate expression. Study the deviation of the approximate expression with respect to the real field. Solve the same problem using a numerical field analysis package such as FLUX2D or FAP. Compare the results obtained with different methods.

11.7  Problem 7

Determine the magnetic field and the vector potential produced by a very long conducting ribbon (sheet), of width a, carrying a longitudinal current of superficial density Js. Generate a procedure for computing the magnetic field, in the case in which the sheet is not plane, but rather obtained by the translation of an arbitrary curve described parametrically. Plot the lines of the magnetic field produced by systems of parallel filaments and sheets.

11.8  Problem 8

Determine the magnetic field produced by a coil with a single layer of N turns carrying the current i, having length l and rectangular crossection of sides a and b. Plot the variation of the field on the coil's axis. Study the deviation with respect to the field of the rectangular filamentary conductor (Proposed exercise 3), in terms of the length l.

11.9  Problem 9

Determine the magnetic field produced by a coil with a single layer of N turns carrying the current i, having length l and arbitrary crossection.

11.10  Problem 10

Determine the magnetic field in the interior of a coil with a single layer of N turns, having spherical core of radius a. Generate a procedure for computing the magnetic field produced by coil with axial symmetry, whose generator curve is not circular, but an arbitrary one. Particular case: the conical coil.

11.11  Problem 11

Determine the magnetic field on the axis of a coil of length l, of circular crossection, having the internal radius a and the external radius b, and N turns carrying the current i. Plot the variation of the magnetic field on the axis and study the deviation with respect to the case of the coil with just one layer of turns (a=b). Generalize the result for the case in which the coil has an arbitrary longitudinal crossection (a and b are functions of z).

11.12  Problem 12

Determine the magnetic field produced by a straight very long bar, of polygonal crossection, carrying the longitudinal current i. Plot the magnetic field lines.


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On 16 Feb 2000, 02:04.