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

• np115

#### np115

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.

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.

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.

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.