Abstract
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 ϵ that identifies the type of curve considered (ϵ = −1 hypocycloids and ϵ = + 1 epicycloids).
Highlights
The calculation of the magnetic field due to a steady current in a circuit is one of the exercises that all students in the first-level course of electricity and magnetism must confront
From Eq (10) it can be verified that for large values of n, the magnitude of the magnetic field tends to μ0 I/2a, which corresponds to the magnetic field in the center of a circular loop
We derive a general expresion to compute the magnetic field produced by current-carrying wires with planar hypocycloids and epicycloids shapes
Summary
The calculation of the magnetic field due to a steady current in a circuit is one of the exercises that all students in the first-level course of electricity and magnetism must confront. For this purpose, introductory physics textbooks present Biot-Savart’s (BS) law and Ampere’s law [1–3]. Introductory physics textbooks present Biot-Savart’s (BS) law and Ampere’s law [1–3] These laws are equivalents [4], the elementary texts usually begin the magnetic field calculations using the BS law. In this paper we are going to extend the study carried out by Miranda,
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