# Can the magnetic field at one end of a long solenoid be calculated using Ampère's Law?

I know that at the ends of a long solenoid induced magnetic field is $$B= (μ_0NI)/2$$. This is found by either integration or considering it as a part of a similar long solenoid. But my question is that is there any way of calculating the same result by Ampere's circuital law? (Preferably without considering it as a part of longer solenoid)

• Do you mean in integral form? Commented Aug 31, 2020 at 12:04
• @BioPhysicist Yes. I'm not sure how to apply it in this particular situation Commented Aug 31, 2020 at 12:33
• My guess is that the answer is "no", since Ampère's Law only allows you to completely derive the field in situations where there is a large amount of symmetry. In particular, the traditional derivation of the field of a solenoid via the integral form of Ampère's Law relies on the translational symmetry of the infinite solenoid; this is no longer present for the half-infinite solenoid. Commented Aug 31, 2020 at 13:06
• @MichaelSeifert Answers should be posted as answers, not comments. Unless you were wanting someone else to say what you are saying in an answer? Commented Aug 31, 2020 at 13:12
• @BioPhysicist: This is one of those questions that I'd only feel comfortable posting an answer if I could provide an affirmative answer. Saying effectively "I doubt it, but I don't know for sure" (as I've done above) doesn't seem like a definitive enough answer to me to post it as such — other folks might be smarter than I am and know a way to do it. Commented Aug 31, 2020 at 13:17