In high school and undergraduate physics, magnetic forces are often introduced as not being capable of doing work. In this paper, we explore the truth of this statement, analyzing the work done in various physical scenarios, including the bending of a wire in an external magnetic field, as well as the interaction between magnetic dipoles. In particular, the formation of surface charges and thorough analysis of the Hall force are elaborated. This paper addresses certain misconceptions regarding magnetic forces and work, and is expected to be of interest to students and educators alike.

We prove that 5 − √ 5 8where both bounds are sharp. This gives an affirmative answer to a conjecture of Alzer and Koumandos.

We prove that for all integers n ≥ 1 and ɵ ≤ 8 ≤ π. This result refines inequalities due to Jackson (1911) and Turán (1938).