12.7 Exercise 37

A nonconducting hard rubber circular disk of radius R is painted with a uniform surface charge density $\sigma .$ It is rotated about its axis with angular speed $\omega .$ (a) Find the magnetic field produced at a point on the axis a distance h meters from the center of the disk. (b) Find the numerical value of magnitude of the magnetic field when $\sigma = 1 \text{C}/\text{m}^{2} ,$ $R = \text{20 cm} , h = \text{2 cm} ,$ and $\omega = 400 \text{rad}/\text{sec} ,$ and compare it with the magnitude of magnetic field of Earth, which is about 1/2 Gauss.