Resumen de Beyond the Point Charge: Equipotential Surfaces and Electric Fields of Various Charge Configurations
Jeffrey A. Phillips, Jeff Sanny, David Berube, Anatol Hoemke
A laboratory experiment often performed in an introductory electricity and magnetism course involves the mapping of equipotential lines on a conductive sheet between two objects at different potentials. In this article, we describe how we have expanded this experiment so that it can be used to illustrate the electrostatic properties of conductors. Different configurations of electrodes can be used to show that the electric field is zero inside a conductor as well as within a cavity, the electric field is perpendicular to conducting surfaces, and the charge distribution on conducting surfaces can vary.
Students often have difficulty transitioning from configurations comprised solely of point charges to those that include conductors.1 Rather than applying the ideal conductor model, students often continue to rely on concepts that they just previously studied, such as Coulomb’s law, and ignore the presence of a conductor. The students also often equate charge density with equipotential surfaces, which implies that the charge density cannot vary across an equipotential surface. Not only do these difficulties inhibit student success in electrostatics, they can also impact performance later in the course when electrodynamics and circuits are studied.
We have observed similar behavior among our own students on a quiz administered after class instruction, and prior to the laboratory activities described below. When asked to give the direction of the electric field at various locations around a single point charge or a dipole configuration, 82-90% of the students answered correctly. (The one exception was between the two charges of the dipole, where 64% answered correctly and 26% answered that the field was zero.) When presented with situations with conductors, however, the percentage of students answering correctly dropped. The most revealing configuration was a conductor with an interior cavity that contained an off-center point charge. When asked for the direction of the field outside of the conductor, 22% of the students gave the correct response and 66% gave a response consistent with an isolated point charge and no conducting shell.
To facilitate the development of students’ electrostatics intuition, we developed several laboratory experiments. These experiments allow students to study electric fields and equipotential surfaces near conductors in a visual manner without the need for mathematics. There are a number of experimental ways to visualize and measure the electric field and potential for static two-dimensional configurations.2–4 The method presented here relies on a sheet of conductive paper5 mounted on a wooden board using metal wingbolts to which leads from a power supply can be connected (Fig. 1). Electrodes are drawn on the paper with a conductive silver ink pen, and a potential difference (generally 10 V) is applied to them.
