Think of the rotating disk as a series of concentric rotating rings. Each ring acts as a circular current loop that produces a magnetic field at the center of the disk. Then integrate over all rings to find the total field. What is the expression for the magnetic field at the center of the single circular loop of radius r carrying current I

Explanation:

Let the current in the coil is i and the radius of the coil is r.

The magnetic field due to the single loop is given by

where, i is the current in the circular loop and r is the radius of the loop. The direction of the magnetic field at the centre of loop is given by the Maxwell's right hand thumb rule.  

r=rho l/a where a is the area, l is the length and rho is resistivity so the greater the area the lesser the resistance thats why the earth pin is thicker bcos current follow the shortest path, so less resistive .

no simpler subs form complex ones. synthesise = make