# Biot-Savart's law application

1. Dec 11, 2016

### Fips

1. The problem statement, all variables and given/known data
There's a disc with a current density surface σ, with radius R and angular velocity ω
Find the B

2. Relevant equations
α = vσ=ωrσ

3. The attempt at a solution
I'm having problems understanding why the cross product gives αr

2. Dec 11, 2016

$\vec{u_r}$ is a unit vector. The cross product $\vec{\alpha} \times \vec{u_r}$ is simply $\alpha \hat{z}$. Write out the expression for $dS'$ in terms of $dr$ and $d \theta$ and I think you will see where the "r" in the numerator comes from. Also, express $\alpha$ in terms of $\sigma$ and $r$ and $\omega$ . ($\alpha$ is not a constant). $\\$ editing... Your diagram is hard to read, but I see the disc extends out to radius R. (I initially thought the disc goes from $R_1$ to $R_2$.) $\\$ Once you get these steps in place, you can then evaluate the integrals.

Last edited: Dec 11, 2016