Accuracy of the Java Simulation for the Charge Motion in Electric and Magnetic Fields

Abstract

The accuracy of the Java simulation by the Runge-Kutta method for the charge motion in electric and magnetic fields has been investigated in comparison with the analytical solution. The error of the simulation depends on the time increment, h , used for the numerical calculation. If we use an increment that is larger than the boundary value, the simulation results in a non-accurate image of the charge motion. In this case, the simulation almost results in an underestimation, that is, a motion that is smaller than the real motion. The boundary increment is proportional to the mass of the charge, m , and is inversely proportional to the charge, q , and the magnetic field, B 0 . The empirical results conclude that the image of the charge motion can be obtained accurately by Java simulation using h < 0.2 m / qB 0 .