Non-differential Form of Biot-Savart Law: Comparison and Confusion Clarified

[Chemist@]

What is the non-differential form of the Biot-Savart law? Is it:
B=mi*I/(4R*pi)*(cos(a)-cos(b)) or B=mi*I/(4R*pi)*(cos(a)+cos(b))?

For a infinitely long conductor, the law is:
B=mi*I/(2R*pi) because a=0 and b=pi. So I would say that the correct expression is the one where the cos are subtracted, but I was solving a problem where a point is in the center of a square-like conductor and they used the formula with the addition of cos to get the magnetic field at that point, as with the subtraction the answer would be zero. What equation is the correct one, I am really confused?

 

[mfb]

The Biot-Savart law is an integral along the current flow, therefore the integral will depend on the geometry of your current flow. Also, what are "a" and "b"?

Laplace?[/size]

 

[ScienceAlum]

As mfb mentioned, Biot-Savart Law is dependent on the geometry of the current carriers. The cosines might stem from the fact that there is a cross product in numerator of the Biot-Savart Law. The cross product, between the length of the conductor and the unit vector from the current to the field, or:

$$ \vec{ds} \times \hat{r} $$

Can also be expressed as:

$$ |\vec{ds}| |\hat{r}| cos \theta $$

This could be the reason you were dealing with cosines.

To get a better understanding of the Biot-Savart formula and any other formula in Electricity & Magnitude I'd suggest using:

http://theeqns.com/introduction-to-electricity--magnetism-with-calculus.html

 

[jtbell]

So I would say that the correct expression is the one where the cos are subtracted, but I was solving a problem where a point is in the center of a square-like conductor and they used the formula with the addition of cos to get the magnetic field at that point

Are the angles defined the same way in both cases?