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Frederick Reif and Jill H. Larkin
Many physically important spatial integrals, such as those needed for finding electric or magnetic fields, can be calculated by a simple method based on elementary geometry, without the need to use the techniques of the calculus or advanced theorems (such as Gauss's or Ampere's laws). The method is practically useful, can provide physical insights, and is suitable for mathematically unsophisticated students in introductory courses. We explain this method by applying it to calculate the electric fields due to a uniformly charged plane, line, and spherical surface.
American Journal of Physics: Volume 44, Issue 6, Pages 515-518
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<a href="https://www.compadre.org/portal/items/detail.cfm?ID=2827">Reif, Frederick, and Jill Larkin. "Physically important integrals without calculus." Am. J. Phys. 44, no. 6, (June 1, 1976): 515-518.</a>
AIP Format
F. Reif and J. Larkin, , Am. J. Phys. 44 (6), 515 (1976), WWW Document, (https://doi.org/10.1119/1.10388).
AJP/PRST-PER
F. Reif and J. Larkin, Physically important integrals without calculus, Am. J. Phys. 44 (6), 515 (1976), <https://doi.org/10.1119/1.10388>.
APA Format
Reif, F., & Larkin, J. (1976, June 1). Physically important integrals without calculus. Am. J. Phys., 44(6), 515-518. Retrieved December 17, 2025, from https://doi.org/10.1119/1.10388
Chicago Format
Reif, Frederick, and Jill Larkin. "Physically important integrals without calculus." Am. J. Phys. 44, no. 6, (June 1, 1976): 515-518, https://doi.org/10.1119/1.10388 (accessed 17 December 2025).
MLA Format
Reif, Frederick, and Jill Larkin. "Physically important integrals without calculus." Am. J. Phys. 44.6 (1976): 515-518. 17 Dec. 2025 <https://doi.org/10.1119/1.10388>.
BibTeX Export Format
@article{
Author = "Frederick Reif and Jill Larkin",
Title = {Physically important integrals without calculus},
Journal = {Am. J. Phys.},
Volume = {44},
Number = {6},
Pages = {515-518},
Month = {June},
Year = {1976}
}
Refer Export Format
%A Frederick Reif %A Jill Larkin %T Physically important integrals without calculus %J Am. J. Phys. %V 44 %N 6 %D June 1, 1976 %P 515-518 %U https://doi.org/10.1119/1.10388 %O text/html
EndNote Export Format
%0 Journal Article %A Reif, Frederick %A Larkin, Jill %D June 1, 1976 %T Physically important integrals without calculus %J Am. J. Phys. %V 44 %N 6 %P 515-518 %8 June 1, 1976 %U https://doi.org/10.1119/1.10388 Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
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The AIP Style presented is based on information from the AIP Style Manual. The APA Style presented is based on information from APA Style.org: Electronic References. The Chicago Style presented is based on information from Examples of Chicago-Style Documentation. The MLA Style presented is based on information from the MLA FAQ. |
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