Abstract: The second question in the 2023 China Undergraduate Physics Tournament (CUPT) “Oscillating sphere” requires the study of the motion of a surface conductive sphere in a magnetic field. Starting from the Maxwell equation system and based on the properties of good conductors, this article uses series expansion and separation of variables method to transform the problem into a Poisson equation with fixed boundaries. Then, using the spherical harmonic function under tensor expression, the force and torque of a non ferromagnetic conductive spherical shell in a uniform magnetic field and a linear gradient magnetic field are studied, and a complete differential equation describing the motion mode of the conductor spherical shell in a linear gradient field is obtained, We solved and designed experiments to explore several special solutions of the dynamic equation. Under the conditions of university physics experiments, we demonstrated the attenuation of the translational and rotational motion of the conductor ball model, as well as the coupling motion between them.

Key words: CUPT, IYPT, magnetic field, spherical harmonic function