Question

Hi, Anyone can help me .
a circular disk of radius R has a surface charge density, and rotated around one of its diameters with velocity w, calculate the magnetic field B in the center of the disc. Thanks

Answer 1

gud question! i had to think a lot...but here's the solution:
total charge on disk: \[Q=\sigma(\pi r ^{2})\]
divide the disk into concentric rings of width dr.
period of rotation:\[T=(2\pi/\omega)\]
current within ring:\[dI=(dQ/T)=\sigma(2\pi rdr)\omega/2\pi=\sigma \omega rdr\]
magnetic field due to each ring: \[dB=\mu_0/4\pi*(\sigma \omega rdr*2\pi r)/(x^{2}+r ^{2})\]
integrate dB under the limits 0 to R and its done!