Electroscope

The device shown to the left consists of two parallel aluminum plates, one of which can pivot on a potentiometer which allows for a digital angle measurement. In the initial state, both plates rest touching each other and the angle reading is set to zero degrees. One of the plates is connected to a Van De Graff generator, transfering charge from the generator onto the plates, thereby causing them to move apart, producing a reading on the digital angle readout. The goal of this project was to analyze the electric field of a finite charged plate and verify the theoretical results by experiment.

The images to the left show a vector field representing the electric field produced by a finite uniformly charged plate which was generated by numerically taking a gradient via a central difference technique of a complicated voltage function.

These equations allow one to relate the voltage on the Van de Graff generator to the separation distance, d, between the plates. Given that we are working with electrostatics and that we are solving Laplace’s equation (del(V)=0) a Schwarz-Christoffel conformal map can be used to include effects of the tilted plate.