## hosein Group Title hi we have a disk with uniform charge density "sigma" that rotate around of axis that transmitted from it's origin,find magnetic moment of disk? 2 years ago 2 years ago

1. gogind

Ok, Total charge on the disk is: $\ Q=\sigma \pi R^2$where R is the radius of the disk If you divide the disk into small rings(width dr) you can write the current in that ring as:$\ dI=\frac{dQ}{T}$where T- time period Since $\ dI =2 \sigma \pi rdr$ and $\ T=\frac{2\pi}{\omega}$ you can rewrite dI as:$\ dI =2 \sigma \pi rdr \frac{\omega}{2 \pi}$$\ dI = \sigma r \omega dr$ Magnetic moment is defined as: $\ m=IA$ where I-current, A-area $\ dm=dI \pi r^2$$\ dm= \sigma r \omega dr \pi r^2$$\ \int dm= \int \sigma \omega \pi r^3 dr$$\ m=\frac{\pi}{4}\sigma \omega R^4$ That would be it.

2. gogind

Also, put a hat on m and omega, since it is a vector...

3. hosein

thnx