While applying Ampere's law to derive the magnetic field of a solenoid,
why can we consider $\vec{\bf B }$ to be zero just outside the solenoid?
For example here it says "Only the upper portion of the path contributed to the sum because the magnetic field is zero outside..". What is the proper justification for this statement?
[Physics] Why is the magnetic field outside a solenoid considered zero
electromagnetisminductancemagnetic fields
Best Answer
For an infinite solenoid, you can argue by symmetry that the $B$-field outside the solenoid has to be parallel to the axis. From this, by varying the size of the loop used in Ampere's law, you can show that the $B$-field outside the solenoid (whatever strength it is) does not vary with distance from the solenoid.
It's pretty easy to show that the $B$-field goes to zero from a solenoid, even an infinite one, as the distance from the solenoid goes to infinity. And so the $B$-field has to be uniformly zero outside the solenoid.
For a finite solenoid, if you are not close to the ends, you can argue that the missing parts of the infinite solenoid shouldn't affect the $B$-field much, and so the field is weak outside the solenoid as compared to inside.