What is the Surface Current and Magnetic Field for a Rotating Charged Disc?

AI Thread Summary
The discussion focuses on calculating the surface current density K(x,y) for a uniformly charged rotating disc with total charge Q and angular velocity w. It suggests using cylindrical coordinates to express K in terms of r and φ, where r is the radial distance and φ is the angular coordinate. For part (b), the application of the Biot-Savart law is proposed to determine the magnetic field at specific points along the z-axis. The magnetic field calculations will be conducted for both r = sk and r = -sk. Understanding these concepts is crucial for solving the problem effectively.
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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 law of Biot and Savart, determine the magnetic field at point r=sk, k is the vector direction. find the same for r=-sk.

Homework Equations


The Attempt at a Solution

 
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i might add that we can use cylindrical coordinates, expressing this as K(r,phi) where r=sqrt(x square + y square) and phi = tan inverse (y/x). this is for part (a).
 
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