Why Does Ampere's Law Use BL Instead of B(2L) for a Solenoid?

In summary, the conversation discusses the use of an infinite solenoid as an example for wrapping wire around a pipe with current I. The amperian path is made into a rectangle, with half inside the solenoid and half outside. The website provided has a diagram of this setup. There is a question about the equation BL=(mu)NI and why it is not B(2L)=(mu)NI. It is explained that there is no field outside the solenoid, so the extra L does not contribute to the integral. The answer is that the L inside the solenoid is being counted.
  • #1
cragar
2,552
3
Lets take the infinite solenoid for example. Where we wrap wire around a pipe with current I.
We make our amperian path a rectangle, half inside the solenoid half out.
This site has the diagram I am talking about, a 1/4 way down the page.
http://teacher.pas.rochester.edu/phy122/Lecture_Notes/Chapter31/chapter31.html
This is probably a dumb question but why is it BL=(mu)NI
why is it not B(2L)=(mu)NI
It seems to me that it would be 2L because for our box we had to go all the way around to enclose the current.
 
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  • #2
cragar said:
It seems to me that it would be 2L because for our box we had to go all the way around to enclose the current.
But there's no field outside the solenoid, so that extra L does not contribute to the integral.
 
  • #3
ok thanks so we are counting the L inside the solenoid.
 

1. What is Amperes Law?

Amperes Law, also known as Ampere-Maxwell Law, is a fundamental law in electromagnetism that describes the relationship between the electric current and the magnetic field produced by that current.

2. How is Amperes Law different from Faraday's Law?

Amperes Law deals with the magnetic field produced by an electric current, while Faraday's Law deals with the electric field induced by a changing magnetic field.

3. What is the mathematical formula for Amperes Law?

The mathematical formula for Amperes Law is ∮CB•ds = μ0∫SJ•dA, where ∮CB•ds represents the line integral of the magnetic field B around a closed loop C, μ0 is the permeability of free space, and ∫SJ•dA represents the surface integral of the current density J over a surface S enclosed by the loop C.

4. How is Amperes Law used in practical applications?

Amperes Law is used in various practical applications such as designing electromagnets, motors, and generators. It is also used in the study of electromagnetic waves and their propagation.

5. Are there any limitations to Amperes Law?

Yes, Amperes Law is only valid for steady electric currents, meaning the current must be constant over time. It also does not take into account any displacement currents, which are present in changing electric fields.

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