Problem with Understanding Ampere's Law

In summary, in a conversation about using Ampere's law, a person encountered a problem due to their lack of understanding. The equation \oint B.dl=uI was derived by defining a point in the middle of a potato shaped loop and integrating with respect to rdθ. However, when trying to apply the same approach to a circular loop, the person was getting an incorrect answer of uI instead of \frac{uI}{2r}. They realized that they needed to use B=\frac{uI}{4πr^{2}} instead of B=\frac{uI}{2πr} and asked for an explanation as to why. They later figured out their mistake and the conversation was resolved.
  • #1
Mr-R
123
23
Dear all,

I am trying use Ampere's law and came across a problem which is a result of my lack of understanding.

[itex]\oint[/itex] B.dl=uI
My lecturer derived the above equation by defining a point in the middle of a potato shaped loop. Where he stated that dl in this case is just rdθ. (r is the line joining dl to the point defined in the middle). And using B=[itex]\frac{uI}{2πr}[/itex] he integrated it with respect to rdθ from θ=0 to 2π to get [itex]\oint[/itex] B.dl=uI.

Now, I am trying to do the same for a circular loop. Obviously I got the same answer uI. But its wrong as it should be [itex]\frac{uI}{2r}[/itex]. The problem is that I am using the same approch he used for the general shape but not getting the same answer. I am using B=[itex]\frac{uI}{2πr}[/itex] where I should actually use B=[itex]\frac{uI}{4πr^{2}}[/itex]

Could someone explain why can't I do that?

P.s sorry if this is messy. It is my first time.
Rashid
 
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  • #2
I think I got it guys. Mods can close this.
 

Related to Problem with Understanding Ampere's Law

1. What is Ampere's Law and why is it important?

Ampere's Law is a fundamental law in electromagnetism that relates the magnetic field created by a current-carrying wire to the current passing through it. It is important because it allows us to calculate the magnetic field in various situations and is essential in understanding the behavior of electric currents and magnetic fields.

2. What is the problem with understanding Ampere's Law?

The main problem with understanding Ampere's Law is that it is not always applicable in all situations. It is based on the assumption of infinitely long straight wires and does not take into account other factors such as the shape and size of the current-carrying wire.

3. How does Ampere's Law differ from Faraday's Law?

Ampere's Law and Faraday's Law are two different laws in electromagnetism. Ampere's Law relates the magnetic field to the current whereas Faraday's Law relates the electric field to the changing magnetic field. In other words, Ampere's Law is used to calculate the magnetic field while Faraday's Law is used to calculate the induced electric field.

4. Are there any exceptions to Ampere's Law?

Yes, there are exceptions to Ampere's Law. As mentioned earlier, it is not applicable in all situations and only holds true for infinitely long straight wires. It also does not take into account the magnetic field created by changing electric fields, which is accounted for by Maxwell's correction to Ampere's Law.

5. How is Ampere's Law used in practical applications?

Ampere's Law is used in various practical applications such as in the design of electric motors, generators, and transformers. It is also used in medical imaging techniques such as MRI machines and in the production of magnetic storage devices like hard drives. Additionally, it is used in the study of Earth's magnetic field and in the development of new technologies like magnetic levitation trains.

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