Ampere's Law -- What is the meaning behind each part?

In summary, the conversation discusses the use of Ampere's and Gauss's laws to calculate the electric and magnetic fields created by a wire and a charged sphere. It is mentioned that the wire creates a uniform magnetic field due to symmetry, and Ampere's law can be used to calculate the field at a point outside the wire. The relevance of the equations S B · dl = u0I and E (4 π a2) or E (4 π b2) in these calculations is also discussed.
  • #1
np115
5
3
Homework Statement
So I know that SB · dl = u0I (sorry this is the only way that was working). But I was wondering what each part meant? Cause in Gauss's law, the SE · dA is the object that is being used to calculate electric field and in Ampere's, it is meant to be similar. So if we had a wire of radius a. This wire creates a uniform field. If we had to calculate the field at point b outside the wire, what would the equation look like? From what I have learned, we would use a circle for this. So B(2pi a) or B(2pi b)?
Relevant Equations
S B · dl = u0I
I believe it would be B(2pi b) but I'm not sure how exactly to explain why.
 
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  • #2
np115 said:
Homework Statement:: So I know that SB · dl = u0I (sorry this is the only way that was working). But I was wondering what each part meant? Cause in Gauss's law, the SE · dA is the object that is being used to calculate electric field and in Ampere's, it is meant to be similar. So if we had a wire of radius a. This wire creates a uniform field. If we had to calculate the field at point b outside the wire, what would the equation look like? From what I have learned, we would use a circle for this. So B(2pi a) or B(2pi b)?
Relevant Equations:: S B · dl = u0I

I believe it would be B(2pi b) but I'm not sure how exactly to explain why.
You need to read Ampere's law carefully.
 
  • #3
np115 said:
This wire creates a uniform field. If we had to calculate the field at point b outside the wire, what would the equation look like?
No wire creates a uniform magnetic field.
If you wanted to calculate the electric field due to a charged sphere of radius ##a## at point ##b## outside the sphere, would you use ##E (4 \pi a^2)## or ##E (4 \pi b^2)## on the left hand side of the equation for Gauss's law? Why?

I agree with @rude man: study Ampere's law some more and pay attention to how it is used in your textbook's examples.
 
  • #4
Of course a single current-conducting wire doesn't create a uniform magnetic field, but you can use symmetry for the simple case of an infinitely long wire. You know by symmetry that the magnetic field is always of the form ##\vec{B}(\vec{r})=B(R) \vec{e}_{\varphi}##, where I've put the wire along the ##z##-axis of a cylinder-coordinate system ##(R,\varphi,z)##.

To get ##B(R)## just use Ampere's circuital law with a circle of radius ##R## around the ##z##-axis in a plane perpendicular to the ##z##-axis.
 

1. 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 that loop. It was first formulated by French physicist André-Marie Ampère in the 19th century.

2. What is the meaning behind the "closed loop" in Ampere's Law?

The closed loop in Ampere's Law refers to a path that completely encloses the area where the electric current is flowing. This can be a physical loop or any arbitrary closed surface.

3. What is the significance of the electric current in Ampere's Law?

The electric current is a crucial component in Ampere's Law as it is the source of the magnetic field. The strength of the magnetic field is directly proportional to the amount of current passing through the closed loop.

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

Ampere's Law and Gauss's Law are both fundamental laws in electromagnetism, but they describe different aspects of the relationship between electric and magnetic fields. Ampere's Law relates the magnetic field to the electric current, while Gauss's Law relates the electric field to the electric charge.

5. Can Ampere's Law be used to calculate the magnetic field at any point in space?

No, Ampere's Law can only be used to calculate the magnetic field along a closed loop where the electric current is known. It does not provide information about the magnetic field at individual points in space.

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