Engineering Physics 2017; 2(1): 25-28 http://www.sciencepublishinggroup.com/j/ep doi: 10.11648/j.ep.20170201.15 Force Generated by a Magnetic Field Applied on a Circular Conductive Turn Rotated in Two Cartesian Axes Romualdo S. Silva Department of Physics, Federal University of Sergipe, São Cristóvão, Brazil Email address: romu.fisica@gmail.com To cite this article: Romualdo S. Silva. Force Generated by a Magnetic Field Applied on a Circular Conductive Turn Rotated in Two Cartesian Axes. Engineering Physics. Vol. 2, No. 1, 2017, pp. 25-28. doi: 10.11648/j.ep.20170201.15 Received: December 7, 2016; Accepted: January 16, 2017; Published: February 13, 2017 Abstract: This article presents a very detailed resolution of a non-trivial problem in Electromagnetic Theory. The problem basically consists of a circular conducting loop of radius R, which has a current I, and is located with its center at the origin of the Cartesian coordinate system. It is rotated with respect to the normal to its plane with angles of θ 0 and φ 0 in spherical coordinates, in addition, there is an applied External Magnetic Field. The forces generated by the magnetic field in all directions were calculated without approximations, where in the z direction the force is zero, as expected. Keywords: Magnetic Field, Circular Loop, Rotation, Force 1. Introduction Classical electromagnetic theory, together with classical mechanics and quantum mechanics, constitute a core of extremely important disciplines for undergraduate and graduate students in physics [1-3]. The mathematical tool used in these courses usually involves vector calculations, ordinary and partial differential equations, Fourier series, Laplace transformations, among others [4-6]. Mechanics tells us as a system that is subject to a certain Force. We know that there are for the moment only the fundamental forces in Physics, which are: Strong, Electromagnetic, Weak and Gravitational, are written from stronger to weak, respectively [7, 8]. Strong forces are the ones that keep protons and neutrons attached to the atoms, they have an extremely short range, but they are a hundred times stronger than the electric forces. The Weak force, which is of the radioactive decay, not only has a short range, but is also much weaker than the electromagnetic. As for Gravitational, it is such a despicable one, that it is only due to great concentrations of masses, like the Earth and the Sun, that we can even perceive it. The laws of electrodynamics were gradually discovered by Franklin, Coulomb, Ampère, Faraday, among others. But who actually completed this task, compacting the equations in a way, was the famous Maxwell [9, 10]. In this way, when we talk about solving problems, many students present difficulties, due to the degree of mathematical complexity present in the exercises, ending up often failing to solve some problems. The main objective of this work is to solve, in a systematic and unprecedented way, an intriguing and quite interesting problem of electromagnetic theory, which is not so trivial but with a certain mathematical capacity we can solve the problem. 2. Calculation of Forces Acting on the Loop The problem basically consists of a circular conducting loop of radius R, which has a current I, and is located with its center at the origin of the Cartesian coordinate system. It is rotated with respect to the normal to its plane with angles of θ 0 and φ 0 in spherical coordinates, as can be observed in Figure 1. In addition, there is an applied external magnetic field, written as follows ( ( 29 0 0 ˆ ˆ (x) 1 1 B B yi B x j η η = + + +   We intend to calculate then the resulting force acting on the loop without making any approximation. We know that by the Law of Biot-Savart [7, 11], when a current with a density ( 29 x J   is in an external magnetic field with a magnetic flux density ( 29 x B   , The law of fundamental force says that the total force on the current distribution is given by [1].