Understanding Biot-Savart's Law for a Rotating Disc with Current Density

[Fips]

Homework Statement

There's a disc with a current density surface σ, with radius R and angular velocity ω

Find the B

Homework Equations

α = vσ=ωrσ

The Attempt at a Solution

I'm having problems understanding why the cross product gives αr

 

[Charles Link]

## \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.