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## Homework Statement

What is the magnetic field a distance z above a rotating disk (ang.velocity w) with surface charge density inversely proportional to the square of the distance from the centre of the disk.

## Homework Equations

K = v*surface charge density

B = (constant)*integral of (K x rhat / r^2 )da

## The Attempt at a Solution

I just want to know if I'm setting up this question right (basically, if I'm setting up the part in the integral correct, which is why i ommited the constant)

charge desntiy = c/s^2 where c is a constant (since it is inversely proportional to square of distance from centre of disk)

so K = v*charge density = ws*c/s^2 = wc/s

so K cross rhat = Ksin(alpha) where alpha is the angle between k and r

but in this case, the angle will always be 90 degrees since k and r are in perpendicular planes

so i need to inegrate (K/r^2)da

but all the horizontal components will cancel so i need to take only the vertical components, so i multiply by cos theta where theta is the angle r makes with the disk

so i have :

integral of (Kcostheta/r^2) da

costheta = s/(s^2+z^2)^0.5

K = wc/s

r^2 = s^2 + z^2

so i get

ingeral of wc/s * s/(s^2+z^2)^3/2 * da

da = sdsdtheta

so I have to integrate (wcs/(s^2+z^2)^3/2)dsdtheta from s=0 to s=R and theta= 0 to theta=2pi

is this correct?