Magnetic field inside a solenoid calculated with Ampere's law

In summary: The law states that the magnetic field at any point is the sum of the magnetic fields generated by current flowing through that point and around the circumference of a loop of that current. The magnetic field at the center of a solenoid is the same as the magnetic field generated by current flowing around the circumference of a loop of current that is centered at the center of the solenoid.
  • #1
Limddong
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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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  • #2
Limddong said:
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.
 
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  • #3
ZapperZ said:
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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  • #4
Limddong said:
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.
 

1. What is a solenoid?

A solenoid is a long, cylindrical coil of wire with multiple turns. It is often used to create a magnetic field when an electric current is passed through it.

2. How is the magnetic field inside a solenoid calculated?

The magnetic field inside a solenoid can be calculated using Ampere's law, which states that the magnetic field around a closed loop is proportional to the electric current passing through the loop.

3. What is Ampere's law?

Ampere's law is a fundamental law in electromagnetism that relates the magnetic field around a closed loop to the electric current passing through the loop. It is named after the French physicist André-Marie Ampère.

4. How does the number of turns in a solenoid affect the magnetic field?

The magnetic field inside a solenoid is directly proportional to the number of turns in the coil. This means that increasing the number of turns will result in a stronger magnetic field, while decreasing the number of turns will result in a weaker magnetic field.

5. Can the magnetic field inside a solenoid be controlled?

Yes, the magnetic field inside a solenoid can be controlled by adjusting the amount of current passing through the coil or by changing the number of turns in the coil. Additionally, the direction of the current can also affect the direction of the magnetic field inside the solenoid.

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