Direction of the normal vector

[Niles]

Hi all

I have two questions.

1) We have the following expression for the currect:

$$I = \int\limits_\mc S {{\bf{J}} \cdot {\rm{d}}{\bf{a}}}$$

Which way does the normalvector in da point? I think it's very crucial, because I might end up with a negative current if I don't get this right.

2) When I want to find the magnetic field a distance s from a wire, which has a current I going through it, I use Ampére's Law. But when I do this, don't I only find the magnetic field caused by a single "disk" in the wire?

Sincerely,
Niles.

 

[nicksauce]

I am pretty sure it should be the outward facing normal.

 

[Niles]

Yes, but there's two ends, so it might go either way?

 

[nicksauce]

Yes... If I have a cylinder that looks like

O---------O

The normal on the left side will be pointing to the left, and the normal on the right side will be pointing to the right.

 

[Raze2dust]

1) depends on what you consider the direction of J.
J is always the direction of the current... So J.da=J* da* cos(theta) will depend on the angle theta

2) its like gauss law..in gauss law..no matter how many charges are present outside, Electric Field on the surface depends on the charge enclosed by the surface only, right?
Similarly here B depends on Ienclosed