# 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.

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!