The Magnetic field for an n-cusped Epi-and Hypo-Cycloids loop current

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We calculate the magnetic field generated by a steady current that takes the shape of two types of special curves: hypocycloids and epicycloids with n numbers of sides. The computation was performed in the center of the referred curves. For this purpose, we use the Biot-Savart law which is studied in every introductory-level electricity and magnetism course. The result is quite general because it is obtained as a function of the number of sides of the curve and in terms of a parameter є that identifies the type of curve considered (є = —1 hypocycloids and є = +1 epicycloids).

Original languageAmerican English
Article numbere20200482
Pages (from-to)1-5
Number of pages5
JournalRevista Brasileira de Ensino de Fisica
Issue number1
StatePublished - 2021


  • Biot-Savart Law
  • Epicycloid
  • Hypocycloid
  • Magnetic field


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