Skip to main content
SpringerLink
Log in

Electrostatic potential of a charged ring: Applications to elliptic integral identities

  • Published:
Journal of the Korean Physical Society Aims and scope Submit manuscript

Abstract

We present a proof of a transformation identity of a complete elliptic integral of the first kind, presented in a recent publication [O. Ciftja et al., Eur. J. Phys. 30, 623 (2009)], where it was derived from an analytical solution of the electrostatic potential due to a uniformly charged ring. In addition, by calculating the electrostatic potential due to a charged ring with a sinusoidal charge distribution, we obtain a new mathematical identity for the complete elliptic integral of the second kind. We show that these two identities can be derived from the existing mathematical identities of elliptic integrals, proving them in a direct manner.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. W. Jr. Jewett and R. A. Serway (ed), Serway’s Principles of Physics 4th edition (Brooks/Cole-Thomson Learning, Belmont, CA, 2006), Chapter 20.

    Google Scholar 

  2. D. J. Griffith, Introduction to Electrodynamics, 4th edition (Prentice Hall, Englewood Cliffs, NJ, 2013), Chapter 3.

    Google Scholar 

  3. O. Ciftja, A. Babineaux and N. Hafeez, Eur. J. Phys. 30, 623 (2009).

    Article  Google Scholar 

  4. M. L. Boas, Mathematical Methods in the Physical Sciences, 3rd edition (Wiley, New York, 2006).

    MATH  Google Scholar 

  5. G. B. Arfken and H. J. Weber, Mathematical Methods For Physicists, 5th edition (Academic, New York, 2001).

    MATH  Google Scholar 

  6. P. M. Morse and H. Feschbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953), p. 1263.

    Google Scholar 

  7. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products 8th eitionn (Academic Press, New York, 2015), p. 668.

    Google Scholar 

  8. Gradshteyn op.cit., p. 873.

  9. H. Hancock, Elliptic Integrals (Nabu Press, New York, 2010), p. 73.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Chonnam National University, Gwangju, 61186, Korea

    Heung-Ryoul Noh

Authors
  1. Heung-Ryoul Noh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Heung-Ryoul Noh.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Noh, HR. Electrostatic potential of a charged ring: Applications to elliptic integral identities. Journal of the Korean Physical Society 71, 37–41 (2017). https://doi.org/10.3938/jkps.71.37

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3938/jkps.71.37

Keywords

Search

Navigation