Consider the following field

The field exists only in the core of the cylinder, a section of which is shown below. Outside, the field is zero. The base of the cylinder is a circle of radius a.

Determine the following:

2.1 Magnitude of F at r = and

2.2 Dot product of F and r.

2.3 ) Divergence of F in the cylinder core.

2.4 Flux, F. ds, coming out from the side.

2.5 Curl of F in the cylinder core.