A circular metal disc of radius R lies perpendicular to a non-uniform magnetic field directed along its axis. The magnitude of the field varies with the radial distance r from the centre according to B(r)=B0Rr, where B0 is a constant.
(i) Write an expression for the elemental magnetic flux dΦ passing through an annular ring of radius r and width dr on the disc.
(ii) Integrate this expression from r=0 to r=R and obtain the total magnetic flux Φ through the entire surface of the disc in terms of B0 and R.