#### Document Type

Honors Project

#### First Advisor

Dr. Jason E. Ybarra

#### Degree Award Date

Spring 2020

#### Keywords

Helmholtz Coil, Magnetic Field, B-Field, Elliptical Coils, Charged Particle in Magnetic Field.

#### Disciplines

Applied Mathematics | Engineering Physics | Other Physics

#### Abstract

A Helmholtz coil is a scientific instrument named\cite{Math} after Hermann von Helmholtz, a German physicist, philosopher, and physiologist who studied electromagnetism. It is actually a pair of coils placed parallel to each other designed to produce a relatively uniform magnetic field when a constant and equal electrical current is sent through them in the same direction. There are numerous applications for these coils which range from measuring the charge to mass ratio of an electron to measuring the strength of a permanent magnet to cancelling out the Earth’s magnetic field to produce a near zero magnetic field region useful for some very sensitive experiments.

While there are many studies and experiments on how perfectly circular Helmholtz coils function, there is little research on modified or altered Helmholtz coils. In this project I investigate a squashed or elliptical version of these coils and research how the magnetic field would depend on the shape of the coils. Also, I investigate how the mathematics change in this scenario given that the assumption of circular symmetry can no longer be used.

This project consists of two parts. The first part is a mathematical derivation of the magnetic field in both a perfectly circular and elliptical coil. Numerical calculations using Python provide visualization of the field and allow me to analyze how the field varies in the space between the coils. For the second part of this project, I produce a computer simulation to show how the magnetic field would affect a moving charge within it using GlowScript. I compare the orbits of the care to that of the case with an ideal uniform field. This simulates the typical configuration for the charge to mass ratio experiment done in undergraduate physics.

#### Recommended Citation

Shumeyko, Sergey, "Investigation of Regular and Non-Axisymmetric Helmholtz Coils: Magnetic Field Structure and Behavior of Charged Particles Within Them." (2020). *Honors Projects*. 21.

https://digitalcommons.bridgewater.edu/honors_projects/21