# More on magnetic field outside an infinite solenoid

The standard argument about the vanishing of the magnetic field outside an infinite solenoid pertains to the longitudinal component, parallel to the solenoid axis. But there must be a non-zero toroidal field. However tightly the solenoid is wound, there is a net current in the longitudinal direction. Thus, by Ampere's law, there is a toroidal $$B$$ field whose magnitude dies off as $$1/r$$. Why is this field never mentioned? Or am I wrong?