always do the calculations in SI units, which means radians/second
Figure 2 of the pdf shows everything you want regarding the physics involved.
The faraday disc is rotting at angular velocity
The magnetic field is perpendicular to the faraday disc and pointing toward up, out of the page.
Charge Q feels 2 forces, the electric force, -eE and the magnetic force, -evB. E, v and B are vectors.
The between the v and the B indicates the vector product of the two vectors, v and B.the arrows indicate the direction of the electric force and the magnetic force.
The arrow pointing at the v indicated the direction of the velocity at the point on the disk, at that instant.
Moving a conductor in a magnetic field forces some of the electrons that are free to move about in the conductor to move. In this case with this geometry, the free electrons move toward the inside edge. This sets up a potential difference, called an ElectroMotiveForce, or EMF, between the inside and outside of the disc. It also produces an electric field in the disc that opposes the movement of the electrons toward the outer edge. Hence the electric force point toward the outside edge, while the magnetic force points toward the inner edge.
The disc has an inner radius of a, (the radius of the axel) and an outer radius of b.
At some point, the electric force and the magnetic force are equal, and the electrons in the disc are at equilibrium.
Equation 2 page 173 shows the relationship between the radial component of the electric field Er , and the vertical component of the magnetic field, Bz.
The next line down shows the potential between the rim and the axel:
V is the potential (or voltage)
=
Er is the electric field on the radial direction (as shown by the arrow in figure 2)
The dr indicates that one integrates this over the radius, r.
The small a and b are the limits of integration. Recall they are the inner and outer radius of the disc
Because of equation 2, the next = replaces Er with the equivalent expression in terms of the magnetic field.
note the 2 pi in the numerator and the denominator – they’re amount to multiplying by 1
the B integral:
since Bz is constant, take it out of the integral
now integrate 2 pi r dr from the axel to the rim (a to b) – this is the surface area of the disk, less the area of the axel.
Thus this B integral is the surface are of the disc times the magnetic field through the disc, or the magnetic flux, Greek upper case phi with a B subscript.
So the voltage the faraday disc produces becomes equation 3, where the notation was changed from V, electric potential, to curly E, the EMF noted above.
As the paper continues for several more pages, it discusses the details.
as for your frustration, i suggest ( in the most emphatic but gentlest terms possible) that you learn some math and physics