Magnetic Field of a Disk

claimed by Chloe Choi (cchoi70) Spring 2017

The Main Idea

Through this page, you will understand how to solve for the magnetic field produced by a moving charged, circular disk.

First, let us start with the basics. We know that moving charges spread out over the surface of an object will produce a magnetic field. This is similar to the concept of how charges spread out over an object allowed them to produce unique electric fields.

In order to figure out this magnetic field, we will start from the fundamental principles that we have learned already with regards to how magnetic fields are produced. We will then build on that and include the geometry of the object in question, in this a circular disk, in order to solve for the magnetic field produced by this disk.

A Mathematical Model

A disk can be considered as a collection of concentric current loops.

One circular current loop of radius R and current I a distance z; above the center of the loop will produce a magnetic field:

We start with a spinning disk with surface charge density σ. We can treat this as a collection of concentric current loops, with the current at radius r given by

where ω is the angular velocity. The field of the spinning disk is then

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