[10 marks] 3. (a) As shown below, a charged plastic cylinder spins on its axis (i.e., the z-axis) resulting in a
uniform surface current density of Js = Jso. The cylinder has a radius of r = ro, and a
total length of L, meaning it extends from z = 0 m to z = L m. Determine the magnetic flux
density at the origin caused by this spinning cylinder, if this cylinder is surrounded by air.
You may assume that the cylinder is infinitely thin (i.e., it is hollow) and the current flows
on the surface of the cone (i.e., r = ro).
Hint: The following integrals may be of use to you
$$
\int \frac{x dx}{(x^2+a^2)^{3/2}} = -\frac{1}{\sqrt{x^2+a^2}} + C
$$
$$
\int \frac{dx}{(x^2+a^2)^{3/2}} = -\frac{x/a^2}{\sqrt{x^2+a^2}} + C
$$
$$
\int \frac{dx}{\sqrt{(x^2+a^2)^{1/2}}} = ln(x + \sqrt{x^2 + a^2}) + C
$$
To
L
Is
y