# Biot and Savart Integral using Vectors

1. Jul 17, 2015

### eliw00d

How would I go about setting up a Biot and Savart Integral using Vectors?

Here is an exercise we had in class:
I tried to set it up using Vectors, and figured dl to be <-L,L> and r to be <½L, -½L>. After the cross product, I am not sure how to handle the integration, since r can vary. Would it be a double integral, or am I overthinking it?

The instructor gave me the answer, and I have been trying to figure out a way to use Vectors to solve it, since I am fairly comfortable with them. Any help would be appreciated!

2. Jul 17, 2015

### Dr. Courtney

Not a double integral. The sum of two line integrals.

3. Jul 19, 2015

### eliw00d

Alright, so I split it up into two parts, r1 and r2.

Both have a magnitude of L / sqrt(2).
r1 has a direction vector of <√2 / 2, √2 / 2, 0>,
r2 has a direction vector of <√2 / 2, -√2 / 2, 0>.

Then, dl1 is <-L, 0, 0> and dl2 is <0, L, 0>.

Both cross products are L * (√2 / 2) in (-k) direction.

Do I integrate from L to 0 for the horizontal part, and 0 to L for the vertical part?

The answer he supplied is (μ0 / 4π) * (I * (√2 / L)) in (-k) direction, but I am not getting the same answer.