Biot Savart Law with a surface current

[OmarRod]

Homework Statement

There is a disc with radius R which has a uniformly-distributed total charge Q, rotating with a constant angular velocity w.

(a) in a coordinate system arranged so that the disc lies in the xy plane with its center at the origin, and so that the angular momentum point in the positive z direction, the local current density can be written J(x,y,z) = K(x,y) d(z). determine the surface current K(x,y) in terms of Q, w, and R.

(b) using the Biot Savart law, determine the magnetic field at point r=sk, k is the vector direction. find the same for r=-sk.

Homework Equations

Biot Savart Law

The Attempt at a Solution

I obtained K= Q(w X R) / pi*R squared for part A, but I'm not sure how that's supposed to fit into the Biot Savart Law.

 

[Lyuokdea]

Note that the velocity of the current is not equal for charges at R/2 as it is for charges at R (the angular velocity is the same, but the radii are different). Try modeling the solution as a sum of current loops of width dr, with approximately equal radius (and thus velocity)

This answer would then be the current, which can be modeled with the Biot-Savart law.

~Lyuokdea

 

[OmarRod]

Note that the velocity of the current is not equal for charges at R/2 as it is for charges at R (the angular velocity is the same, but the radii are different). Try modeling the solution as a sum of current loops of width dr, with approximately equal radius (and thus velocity)

This answer would then be the current, which can be modeled with the Biot-Savart law.

Ok, I've done this and after applying Biot Savart's Law, I get a zero magnetic field. This can't be right can it?

 

[Lyuokdea]

that doesn't sound right...what did you get for J, and how did you include this into the biot savart law?

~Lyuokdea

 

[OmarRod]

nevermind, i looked at it again and found my mistake. thanks!