Deflection of a uniformly charged cantilever rod

Abstract We investigate the deflection of a uniformly charged cantilever rod under the electrostatic influence of a point charge. The distribution of the electrostatic force along the rod follows Coulomb’s law and therefore depends on the position of the point charge. An exact solution can be obtained for both the deflection and slope of the rod. We further demonstrate that approximate solutions, corresponding to different point charge positions, are in good agreement with the exact solution. This study provides a useful example for understanding calculus-based physics at the university level.