Ampere's Law: Current Enclosed in a Volume

In summary, Ampere's Law is used to calculate the magnetic field, and it requires the current enclosed in a volume, not just a surface or loop. This is because current can flow in three dimensions, and Ampere's Law takes into account the direction of the current. Additionally, Ampere's Law states that the current passing through a surface and the current passing through the volume enclosed by that surface will have the same effect on the magnetic field.
  • #1
Yosty22
185
4

Homework Statement



Ampere's Law uses the current enclosed in a:
A) Loop
B) Surface
C) Volume

Homework Equations





The Attempt at a Solution



I think the answer is C because I often see current in 3-dimensions, that is, it can be into or out of the page as well as up/down and left/right. I don't know for sure, but is my thinking correct?
 
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  • #2
Hi Yosty22! :smile:
Yosty22 said:
I think the answer is C because I often see current in 3-dimensions, that is, it can be into or out of the page as well as up/down and left/right. I don't know for sure, but is my thinking correct?

Hint i]: consider a sphere … is there any difference between the current passing through the volume of the sphere and the current passing through the surface of the sphere?

ii] Consider two different surfaces whose edges are the same loop …

what does Ampere's law say about the two currents through those two surfaces? :wink:

(and anyway, what does Ampere's law say about the magmetic field?)
 

1. What is Ampere's Law and what does it state?

Ampere's Law is a fundamental law in electromagnetism that relates the magnetic field generated by a current to the current itself. It states that the magnetic field around a closed loop is directly proportional to the current passing through the loop.

2. 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 and generators. It is also used in the development of magnetic resonance imaging (MRI) technology and in the construction of magnetic levitation trains.

3. What is the equation for calculating the magnetic field using Ampere's Law?

The equation for calculating the magnetic field using Ampere's Law is B = μ₀I/2πr, where B is the magnetic field, μ₀ is the permeability of free space, I is the current, and r is the distance from the current.

4. Can Ampere's Law be used for any closed loop?

No, Ampere's Law can only be used for closed loops that are symmetrical and have a consistent current passing through them. If the loop is not symmetrical or the current is not consistent, other methods must be used to calculate the magnetic field.

5. How does Ampere's Law relate to Gauss's Law?

Ampere's Law and Gauss's Law are both fundamental laws in electromagnetism. While Ampere's Law relates the magnetic field to the current, Gauss's Law relates the electric field to the charge. Together, these laws help us understand the interplay between electric and magnetic fields in various situations.

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