Understanding Gauss's Law Regarding Magnetic Field in Current Sheets

[YusifNurizade]

Hello all,

I've gotten some solid advice on these forums before and I was hoping someone could help me out again.

I'm learning about Gauses's Law and am having some trouble understanding how it pertains to the magnetic field in a current sheet with a width. The online examples I've found with regard to a current sheet talk about infinite sheets that you treat as N number of wires carrying current and boggle down to the following formula:

$B = (\mu IN)/(2)$

My question is whether or not the formula can be modified by substituting the unknown N with a known W (width) or if N can be scrapped with no replacement since there is only one piece carrying the current? Or would the resulting formula be more complicated making me very far off base?

Any help would be appreciated. I am trying to grasp the concept as it applies to multiple conductors not just the generic examples given.

Thanks,
Yusif Nurizade

 

[mikeph]

I would hazard a guess that this formula is the result of an integration of the Biot-Savart law for all the wires in a parallel sheet. If this is correct I think the case of a thick sheet would give a different result, because you will start getting contributions from out-of-plane wires (ie. sqrt(x^2 + y^2) distances rather than just x).

Does your source for this formula contain a derivation? That would probably be very helpful in deriving a "thick conductor" version.

 

[YusifNurizade]

MikeyW,

I'm either unfamiliar or can't recall the Biot-Savart Law although the quick glance I took after reading your message has examples of single wires.

The scenario I am considering involves no given thickness but a known width and infinite length. Later elements of the example include an identical parallel sheet with current running in the opposite direction to derive inductance but so far I am just considering the magnetic field.

A couple of sites document the derivation that got me to the original formula I posted. One of the best documented was on Wikipedia:

http://en.wikipedia.org/wiki/Current_sheet

The example I am studying differs in that it has a known width so I'm trying to figure out how the formula would be adjusted.

Thanks,
Yusif