# Magnetic field inside a solenoid calculated with Ampere's law

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## Main Question or Discussion Point

I think the real magenetic field is sum of the magnetic fields calculated in each cross section of solenoid with various angle and same center axis when i apply Ampere's law. (Imagine the cross section contains a part of center line of the solenoid) Please let me know why we don't do like that. :)

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ZapperZ
Staff Emeritus
I think the real magenetic field is sum of the magnetic fields calculated in each cross section of solenoid with various angle and same center axis when i apply Ampere's law. (Imagine the cross section contains a part of center line of the solenoid) Please let me know why we don't do like that. :)
I'm not clear what you are saying here, especially by the phrase "real magnetic field". Were you calculating an "unreal" magnetic field via other means?

There's nothing to stop you from calculating the magnetic field field at the center of a single circular loop of current, and then summing it up as you add more and more loops to form a solenoid. You'll get the same answer as applying the Ampere's Circuital method. But using the former is a lot more work!

This is no different than using Gauss's law for highly-symmetric situation to find the E-field, instead of applying Coulomb's law and doing all those nasty integrations.

Zz.

I'm not clear what you are saying here, especially by the phrase "real magnetic field". Were you calculating an "unreal" magnetic field via other means?

There's nothing to stop you from calculating the magnetic field field at the center of a single circular loop of current, and then summing it up as you add more and more loops to form a solenoid. You'll get the same answer as applying the Ampere's Circuital method. But using the former is a lot more work!

This is no different than using Gauss's law for highly-symmetric situation to find the E-field, instead of applying Coulomb's law and doing all those nasty integrations.

Zz.
Thanks for answering my question! Yes, the 'real' is not appropriate word. 'Total' would be appropriate.
Sorry for that.... However, what i really want to know is tha, Ampere's law gives us just some magnetic field that is generated by current 'inside' the ampere circuital. That means the magnetic field i got from a cross section of a solenoid by Ampere's law is not total magnetic field. Why we do not consider other cross section's magnetic field to get total magnetic field? They make magnetic field too.

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Mister T
Gold Member
Ampere's law gives us just some magnetic field that is generated by current 'inside' the ampere circuital. That means the magnetic field i got from a cross section of a solenoid by Ampere's law is not total magnetic field.
No, it doesn't. You are not understanding what Ampere's Law asserts.