We can prove that the field of an infinite cylindrical pipe carrying a current along its length is zero on its central axis by using a symmetry argument.

Question

Quizplus · Accepted Answer

Due to the cylindrical symmetry of the system, the magnetic field at any point on the axis of the cylinder must be directed along the axis. However, since the problem is symmetric with respect to inversion along the axis (flipping the direction of the current would not change the physical situation), the magnetic field cannot have a preferred direction along the axis. Therefore, by symmetry, the magnetic field on the central axis of an infinitely long cylindrical pipe carrying a current must be zero.

We Can Prove That the Field of an Infinite Cylindrical