RESEARCH ON THE APPLICATION OF SYMMETRY METHODS IN SOLVING UNIVERSITY PHYSICS PROBLEMS — TAKING MECHANICS, ELECTROSTATIC FIELDS AND STEADY MAGNETIC FIELDS AS EXAMPLES

Abstract

In the knowledge system of university physics, symmetry is widely present in branches such as mechanics and electromagnetism. It is not only a conceptual tool that connects different disciplines, but also demonstrates significant value in solving problems. This paper conducts an analysis through specific examples: In particle kinematics of mechanics, the symmetry of motion is used to equate the trajectory of a small ball’s zigzag elastic collisions inside a well to projectile motion, simplifying multi-process problems into a single model; In electrostatic fields, taking a uniformly charged thin disk as an example, Gauss's theorem is applied in combination with the planar symmetry of the electric field to efficiently solve for the electric field intensity on the axis, avoiding complex integrations; In steady magnetic fields, for an infinitely long current-carrying thin metal plate, Ampère's circuital theorem is utilized, and the mirror symmetry of the magnetic field is employed to simplify the calculation of magnetic induction. The research shows that the symmetry method has the common advantages of "more concise in thinking and analysis, and more efficient in calculation and solution" in solving university physics problems. It can help researchers quickly identify problem-solving paths and reduce the complexity of problems.