# Calculation of boundaries of the working zone of the round magnetic applicator

## Authors

• V. M. Kupriianchuk Taras Shevchenko National University of Kyiv
• M. M. Budnyk Glushkov Institute of Cybernetics of the National Academy of Science of the Ukraine https://orcid.org/0000-0002-4020-0213

## Keywords:

magnetic field applicator, working zone, nanomaterials, nanoparticles localization

## Abstract

We considered the problem of modeling a magnetic applicator of round shape, designed to act on an object (target) with a constant or variable magnetic field. Due to the fact that the magnetic field monotonically decreases with increasing distance to the applicator, the model includes 3 applicators with different radii, and the problem is solved based on their comparison At the same time, the larger and smaller applicators have radii that are larger or smaller than the radius of the average applicator by the same number of times (scale factor k). Analytical dependences on k of the near, far boundary, and middle of the intermediate zone, i.e., the working zone, in which the target should be located, were found in the approximation of the current loop. Asymptotics were found in extreme cases of minimal (k=1) and large (k>>1) scale factors. It is shown that the middle of the working zone at k=1 is equal to R/√2, (R is the radius of the applicator), and at k>>1 it grows as (R/2) k^(1/3). These results provide a solution to the "direct" problem of choosing target parameters for an applicator of a certain radius - size and distance to it. Such a selection is critical when the targets have a sufficiently large size and the distance to which cannot exceed a certain critical value (depth of occurrence), which takes place in particular for the action by magnetic field on certain organs or the area of localization of magnetic (nano)materials inside biological objects, including humans or animals.

Pages of the article in the issue: 86 - 91

Language of the article: Ukrainian

## References

DUDCHENKO, A., ALEKSEYTSEV, A., DUDCHENKO, N., MYKHAILYK, O. (2008) Magnetic applicator for directed delivery of magnetic nanoparticles to the target organ. [Online] p. 1–4 – Available from: https://ojs.ukrlogos.in.ua/index.php/interconf/article/download/14013/12874

BUDNYK M., DUDCHENKO N., DUDCHENKO O., ALEXEYTSEV YU., BUDNYK V. (2008) Magnetic applicator system for concentration of magnetic materials in a local area inside a biological object // Patent UA 29313, publ. 10.01.2008, Bull. "Industrial Property", No. 1, 2008.

JORDAN, A. (1989) Magnetic fluid hyperthermia, Issue. 201: Journal of magnetism and magnetic mat materials. – 1999. – Issue 201. -PP. 413-419.

KUPRIIANCHUK, V.M., BUDNYK, M.M. (2021) Application of magnetic nanoparticles in biology and medicine (review) // Book of Abstracts of VI Intern. Sci. and Practical Conf. “Trends and directions of development of scientific approaches and prospects of integration of Internet technologies into society”. Stockholm, Sweden 2021. Pp. 492-497.DOI: 10.46299/ ISG.2021.I.VI URL: https://isg-konf.com.

KUPRIIANCHUK, V.M., BUDNYK, M.M. (2021) Method of fluorescence visualization of nanoparticles in the body of laboratory animals // Book of Abstracts of XI Intern. Sci. and Practical Conf. “Topical issues of modern science and education”. Tallinn, Estonia 2021. Рp. 202-206. DOI: 10.46299/ISG.2021.I.XI URL: https://isg-konf.com

2022-10-12

## How to Cite

Kupriianchuk, V. M., & Budnyk, M. M. (2022). Calculation of boundaries of the working zone of the round magnetic applicator. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (2), 86–91. https://doi.org/10.17721/1812-5409.2022/2.11

Modern Physics