Question

An insulating circular disk of radius a has a static charge. The disk rotates about its center with an angular velocity w. Find the magnetic field at the center of the disk

Answer 1

zero

Answer 2

ya its zero

Answer 3

actually the B field equals \[(mu _{0 w _{q}}) \div2pir\] but what I wanted to know is how to derive this result.

Answer 4

1. divide the disc in circular strips of radius r and width dr.
2. every strip carries a charge dq = σ 2πr.dr
3. moving charge on the strip is a current di = dq/T = ω dq/2π

that should help you find the magnetic field eventually.

The value is indeed \(\large B_{centre}=\Large \frac{\mu_0\omega \:Q}{2\pi a} \)