According to my book, the magnetic field in any location inside the toroid (the empty region inside the toroid circumference) is zero because if we consider a circular loop passing through that point, the magnetic field would be zero as there is no current inside that loop. If we use this logic for inside the solenoid and take a small circle inside the solenoid with center at axis, we would get the same zero MF there, which is not true. If we apply this logic we will get a zero magnetic field wherever there is no current. I know this is not right and I am missing some point here.
[Physics] Why can’t we consider Amperean loop inside solenoid just like a toroid
electromagnetismmagnetic fields
Best Answer
The Amperian Loop centered at the axis of the solenoid encloses no current. This is true.
You note two rules.
You think 1. and 2. contradict. However, realize that Ampere's Law only describes the net magnetic field along the Amperian Loop. It does not say anything about other magnetic fields. So let's modify the rules.
To see why 1. and 2. are true and don't contradict, let's consider an ideal example, then generalize.
Ideal Example
The magnetic field lines within an infinitely long solenoid are perfectly parallel with the central axis of the solenoid. This is consistent with 2.
If you consider a circle centered at the solenoid's central axis, realize that all magnetic field lines are perpendicular to the circle.
So, there are no magnetic field lines that go along the Amperian Loop. This is consistent with 1.
General Example
In the real world, we can't have infinitely long solenoids. Real world solenoids deviate from the ideal solenoid.
A single wire loop has a circularly symmetric magnetic field. Similarly, a stack of single wire loops have a circularly symmetric magnetic field. This is consistent with rule 2.
Since the solenoid is made up of circles, note that any deviation from the ideal must be circularly symmetric.
By circular symmetry, there is no net magnetic field along the circular Amperian Loop. This is consistent with rule 1.
Conclusion
Rules 1 and 2 hold for all solenoids, and don't contradict each other.
(P.S. I'm pretty sure, but cannot prove, that real-world solenoids have magnetic field lines that deviate radially outwards from the central axis, radially perpendicular to the Amperian Loop. So, there is no single magnetic field line that contributes to the Amperian Loop, and we don't even need to consider circular symmetry.)