Axial component of the magnetic field produced by a straight solenoid: Application of the solid angle concept

Abstract

The magnetic field along the axial direction for a straight solenoid at an arbitrary point is shown to be directly proportional to the solid angle subtended by the current carrying surface. The result is true anywhere, i.e., on the axis or off-axis, for a finite or an infinite solenoid as long as it is straight and the current density is uniform. The geometrical relationship is applied to several special situations where surprising results are easily obtained and discussed.