THEORETICAL CALCULATIONS OF THE MAGNETIC FIELD OF HELMHOLTZ COIL

Аннотация

In the present article we have studied the physical properties of a Helmholtz coil that can produce a second-order uniformity field for use in magnetic resonance imaging (MRI) applications. A Helmholtz coil is a device used to create a region of nearly uniform magnetic field. It consists of two identical magnetic coils arranged symmetrically along a common axis, one on each side of the experimental site, separated by a distance equal to the radius of the round coil and the half-length of the side of the square coil. Each coil carries an equal electric current flowing in the same direction. The main goal of this article is to calculate the magnetic field created by Helmholtz coils at any point in space. Mathematical equations are simulated using the MATLAB simulation tool to demonstrate the axial magnetic field generated by one and two loops. The importance of testing electronic devices under the influence of a constant magnetic field is substantiated. The magnetic field created by Helmholtz coils of finite rectangular cross-section is investigated. An analytical expression is derived for the magnetic field on the axis of a solenoid of finite thickness and the magnetic field on the axis of Helmholtz coils of rectangular cross-section. In the particular case of using Helmholtz coils with a square cross-section, the condition for the second derivative of the magnetic field to vanish along the symmetry axis of the system at its center is numerically analyzed. This makes it possible to determine the distance between square coils at which the field in the center of the system is most uniform. It is shown that taking into account the finiteness of the cross-section leads to a change in the optimal distance between the coils. A table of optimal distances for square Helmholtz coils of different thicknesses has been compiled.