Investigating Charged Particle Dynamics & Weber’s Force Law
- Funding
- Self-funded
- Study mode
- Full-time
- Apply by
- Start date
- Year round
- Subject area
- Electrical Engineering and Electronics
Are you fascinated by electromagnetism, fundamental physics, and charged particle dynamics? This self-funded PhD offers an exciting opportunity to explore the force law of Wilhelm Weber—a concept with profound implications across physics and engineering [eg see Ref. 7].
Charged particle dynamics, also known as charged particle optics, focuses on how charged particles (e.g., electrons, protons, ions) interact with electric and magnetic fields. Understanding these interactions is crucial for designing technologies such as particle accelerators, mass spectrometers, electron microscopes, fusion reactors, and medical treatments like proton beam therapy.
This PhD will investigate Weber’s force law, an elegant extension of Coulomb’s law that describes forces between moving charges. While historically explored in electromagnetism, its potential significance in mechanics, cosmology, and quantum physics remains an open question. Depending on your interests, the project can also explore other alternative force laws, such as Ampère’s or Ritz’s force laws.
There is scope to tailor the research to your strengths, whether in theoretical exploration, experimental validation, or a combination of both.
The successful applicant is expected to start in 2025, although this date is negotiable.
This project is open to self-funded UK and international applicants. We welcome applicants with a background in physics, applied mathematics, electrical engineering, or a related field. A strong interest in electromagnetism, charged particle dynamics, and fundamental physics is highly desirable.
You should have a degree in physics, mathematics or an engineering discipline. Master’s level students are encouraged to apply. If you have relevant experience (eg 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.
[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. https://royalsocietypublishing.org/doi/10.1098/rspa.2016.0338
[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. http://www.jpier.org/PIER/pier.php?paper=15021106
[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. https://www.jpier.org/PIER/pier.php?paper=21060104
[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). https://www.nature.com/articles/s41598-020-67596-0
[5] Q. Li and Simon Maher, “Deriving an Electric Wave Equation from Weber’s Electrodynamics.” Foundations 2023, 3, 323-334. https://doi.org/10.3390/foundations3020024
[6] C. Baumgärtel and Simon Maher. “Resolving the paradox of unipolar induction: new experimental evidence on the influence of the test circuit”. Scientific Reports 12, 16791 (2022). https://doi.org/10.1038/s41598-022-21155-x
[7] C. Baumgärtel and Simon Maher, “Foundations of Electromagnetism: A Review of Wilhelm Weber’s Electrodynamic Force Law.” Foundations 2(4), 949-980 (2022). https://doi.org/10.3390/foundations2040065
If you have your own funding (e.g., scholarship, sponsorship, etc) and are interested, please email Professor Simon Maher (s.maher@liverpool.ac.uk) and attach a copy of your CV.
You may need the following documents to complete your online application:
Finally, register and apply online. You'll receive an email acknowledgment once you've submitted your application. We'll be in touch with further details about what happens next.
Your tuition fees, funding your studies, and other costs to consider.
Fees apply to academic year 2025/26.
*Please note: if you’re an international student undertaking a PhD within the Faculty of Science and Engineering, the fee you pay will reflect the nature of your research project. Some research projects incur a higher fee than others, for example if you’re required to undertake laboratory work. You’ll be informed of the fee for your intended PhD in your offer letter.
We understand that budgeting for your time at university is important, and we want to make sure you understand any costs that are not covered by your tuition fee. This could include buying a laptop, books, or stationery.
Find out more about the additional study costs that may apply to this 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 (eg government scholarship, industry sponsorship, self-funding).
The successful applicant will be expected to provide the funding for tuition fees, living expenses, plus a research bench fee of approximately £1,500 per year.
If you're a UK national, or have settled status in the UK, you may be eligible to apply for a Postgraduate Doctoral Loan worth up to £30,301 to help with course fees and living costs.
There’s also a variety of alternative sources of funding. These include funded research opportunities and financial support from UK research councils, charities and trusts. Your supervisor may be able to help you secure funding.
My qualifications are from United Kingdom.
We offer a range of scholarships and bursaries that could help pay your tuition fees and living expenses.
If you’re awarded this prestigious scholarship, you’ll receive significant funding to support your postgraduate research. This includes full payment of your PhD fees and a cash bursary of £17,000 per year while you study. One award is available in each academic year.
If you’re a UK student, either born in or with strong family connections to Merseyside, you could be eligible to apply for financial support worth up to £12,000 per year for up to three years of full-time postgraduate research (or up to five years part-time pro-rata).
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Have a question about this research opportunity or studying a PhD with us? Please get in touch with us, using the contact details below, and we’ll be happy to assist you.