(10 pts) Consider a vector field given in the cylindrical coordinate system by the expression:

F(x, y, z) = zf + ro + 2

a) Calculate the line integral of F. dl for a closed circular contour located entirely on the

z = 0 plane and a radius of a going in the direction indicated by the arrow in the figure

below. Let's verify the Stokes theorem (VxF). ds = fF.dl. Calculate the curl of

vector F, i.e.V x F. Calculate the flux of the curl of the vector F (ff (V × F). ds) through

the circular surface that is located entirely in the z = 0 plane and is bounded by the circular

contour shown in the figure above. Use+z as the direction of vector ds./ndirection of

travel

b) Calculate by any method the flux of the curl of the vector F through the surface which

upper half of a spherical shell (centered at the origin) as shown in the figure below.

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