Magnetic flux, current and magnetic field confusion

In summary, the conversation discusses the use of dl as a length element in Ampère's law and how it differs from its use in Gauss' law. The confusion arises from the constant 2π being used in both cases, but the conversation ends with a resource that may help clarify the situation.
  • #1
Cocoleia
295
4
1. The problem statement

Relevant equations: I am confused. When dealing with Ampères law:
upload_2017-4-25_13-23-13.png

dl is supposed to be the length element? Like when we have Gauss' law for electric fields and we use a circular Gaussian surface, we have E(4πr^2)=Qenclosed/ε
So in this case, when we have a circular loop our dl will be 2πr, since that is the circumference of the loop ? Or do I just understand nothing of this type of problem?
I am confused because we seem to use 2π no matter what, like in this problem:
upload_2017-4-25_13-26-19.png


3. The attempt at the solution:
I don't see anyway to include 2π, but they still do:
upload_2017-4-25_13-27-0.png
 

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Related to Magnetic flux, current and magnetic field confusion

1. What is magnetic flux?

Magnetic flux is a measure of the total number of magnetic field lines passing through a given area. It is represented by the symbol Φ and is measured in units of webers (Wb).

2. How is magnetic flux related to current?

Magnetic flux is directly proportional to the amount of current flowing through a conductor. This means that as the current increases, so does the magnetic flux.

3. What is the difference between magnetic flux and magnetic field?

Magnetic flux is a measure of the total number of magnetic field lines passing through a given area, while magnetic field is a measure of the strength and direction of the magnetic force at a specific point in space.

4. How does magnetic flux affect motors and generators?

In motors and generators, magnetic flux plays a crucial role in the conversion of electrical energy to mechanical energy and vice versa. The changing magnetic flux induces an electric current, which is used to power the motor or generator.

5. What causes confusion between magnetic flux, current, and magnetic field?

The confusion between these concepts often arises because they are all related and interconnected. Additionally, they all involve complex mathematical equations and require a thorough understanding of electromagnetism to fully grasp their differences and relationships.

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