Fundamental Electromagnetics: Foundational Theories of Electricity and Magnetism relating to Charged Particle Interactions


Applications are invited for a self-funded PhD.

Charged particle dynamics (also known as charged particle optics) is concerned with the interactions of charged particles (e.g., electrons, protons, ions) within an electric and/or magnetic field. In charged particle optics the prediction of beam trajectories is of great interest for design purposes, such as focusing, guiding elements, filtering, transportation lines, particle accelerators, analytical measurement devices, etc.

The deflection of charged particles by electric and/or magnetic fields has widespread and important connotations in physical sciences, engineering, life sciences and for a wide range of technologies The electrical forces at play between charges is essential for a multitude of high-tech applications, from particle accelerators, electron microscopes, electronics, nuclear fusion reactors, magnetrons and plasma physics, through to medical diagnostics (e.g., radiation therapy, such as proton beam therapy), electron beam welding, mass spectrometry and many others.

The history of electrodynamics has fascinated humanity since ancient times (including the ancient Greeks and other civilisations). Historical advancements have been made over many years by great scientists and engineers, the likes of Gray, du Fay, Franklin, Volta, Ohm, Coulomb, Ampere, Faraday and Maxwell – with many other important contributors besides.

In this PhD project you will undertake research investigating the force law of Wilhelm Weber (whom the SI unit of magnetic flux is named after). Whilst Weber’s force has been predominantly demonstrated in relation to electromagnetic phenomena it has also been shown to have relevance to mechanics, the structure of the atom, gravity, quantum mechanics and cosmology. Weber's force law can be thought of as an extension of Coulomb's force law for charges in relative motion. Weber’s force law is beautifully simple, yet profound with many implications that are yet to be explored.

There is scope to tailor the precise investigations of this PhD research to match the interests of the PhD candidate. There is also scope for the candidate to make a case for the investigation of other interesting theories (e.g., Ampere’s force law, Ritz’s force law, etc.) Candidates who have a predominant interest in either theoretical or experimental work (ideally both) are encouraged to apply. For reference, interested applicants can also peruse a selection of some recent publications in this regard, e.g., refs [1-5].

You should have a degree in physical sciences, mathematics or an engineering discipline. Masters level students are encouraged to apply. If you have a strong Bachelor’s degree or have relevant experience (e.g., prior project experience, work experience, publications, demonstrable interest in the topic, etc.), you are also encouraged to apply. In exceptional circumstances those with a non-traditional educational background will be considered dependent upon relevant experience. A strong interest and familiarity with electromagnetism, applied mathematics, electrical engineering and/or fundamental physics is desirable. Applicants will be considered on a case-by-case basis.

If you are interested, please email Prof Simon Maher ( with the project title in the subject of your email and include a copy of your CV.

Please: this is a self-funded project and requires that the applicant has their own source of funding (e.g., government scholarship, self-funding). PhD fee information is available at: Postgraduate Research - University of Liverpool.


Please note: this project is open to applications year-round until a suitable candidate is found - therefore the listed deadline may be subject to change.


Open to students worldwide

Funding information

Self-funded project

The project is open worldwide, to applicants of any nationality. Please note that this position is unfunded. Therefore, it is required that any applicant should have a funding source in place (e.g., government scholarship), in which case they are encouraged to contact the Principal Supervisor directly to discuss their application and the project.

The successful applicant will be expected to provide the funding for tuition fees and their living expenses, as well as a research bench fee of approximately £1250 per year.

Details regarding the PhD tuition fees (i.e., postgraduate research) can be found on the University website.



[1] R. Smith, F. Jjunju, I. Young, S. Taylor, and Simon Maher. "A physical model for low-frequency electromagnetic induction in the near field based on direct interaction between transmitter and receiver electrons." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2191 (2016): 20160338.

[2] R. Smith, F. Jjunju, and Simon Maher. "Evaluation of electron beam deflections across a solenoid using Weber-Ritz and Maxwell-Lorentz electrodynamics." Progress In Electromagnetics Research 151 (2015): 83-93.

[3] C. Baumgärtel, R. T. Smith, and Simon Maher. “A Novel Model of Unipolar Induction Phenomena Based on Direct Interaction Between Conductor Charges.” Progress In Electromagnetics Research 171 (2021) 123-135.

[4] C. Baumgärtel, R. T. Smith, and Simon Maher. “Accurately predicting electron beam deflections in fringing fields of a solenoid.” Scientific Reports 10: 10903 (2020).

[5] C. Baumgärtel and Simon Maher, “Foundations of Electromagnetism: A Review of Wilhelm Weber’s Electrodynamic Force Law.” Foundations 2(4), 949-980 (2022). Foundations | Free Full-Text | Foundations of Electromagnetism: A Review of Wilhelm Weber’s Electrodynamic Force Law (