Nov 16, 2022
Sometimes the curvature radius of a curve can be found by using physical methods although it seems that you must use calculus to find it. In this article, the curvature radius of the curve x2=2py at the point where the curvature radius is smallest is found by using physical methods without using calculus (with only high school knowledge). The answer is that the smallest curvature is exactly p, and the point with smallest curvature is the vertex.
Nov 16, 2022
In the vacuum, inside a fixed ring of radius R with fixed charge Q uniformly distributed, there is a point charge with charge q and mass m moving in the plane of the ring due tue the electrostatic force. It moves in the small region around the center of the ring, and the motion is periodic along a closed curve. The area of the region enclosed by the curve is S. Denote the distance from the center to the point charge as r, and r≪R. Find the magnetic induction B at the center of the ring.