Abstract
A common problem provided in elementary physics textbooks is the analysis of the circular motion of a point-like particle affected by a gravitational field on the frictionless inner surface of an inverted cone. In this research, we study the motion of a charged particle on the same surface subject to an electric field generated by an electric dipole placed at the bottom of the cone. We study negatively and positively charged particles and analyse the dynamics of both. We calculate the physical quantities such as speed, angular velocity, angular momentum, and mechanical energy. Furthermore, we determine all possible distances travelled by the particles measured from the dipole. We also discuss the stability of the circular orbit using the effective potential. Finally, we consider the particle’s motion on a generic surface formed by the revolution of the curve ρz around the vertical axis. We determine the differential equation of ρz , in which the kinematic variables including speed v, angular velocity ω, and angular momentum L are constant.
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