The transient magnetic field outside an infinite solenoid

Abstract

The electromotive force (emf) in a loop outside an infinite solenoid with changing current is usually calculated using the vector potential because the magnetic field outside an infinite solenoid is supposed to be zero. However, the magnetic field will only be zero for steady currents. A change in the applied voltage will give rise to a change in the current, which will propagate along the solenoid in the same way as a wave on a transmission line. This gives rise to a transient magnetic field outside the solenoid. It is quite possible to calculate this transient magnetic field and use it in Faraday’s law to calculate the emf directly without using the vector potential. In practice, it is usually simpler to use the vector potential. However, care should be taken to ensure that students are not given the impression that there is no magnetic field and that it is the vector potential that acts on charges in the loop. We give examples of the magnetic field configuration outside an infinite solenoid for a steplike change in driving voltage and for an ac driving voltage.