Self Assessment Quiz

1. If a vector field  is given by , where M, N and P are functions of x, y and z, show that the field is conservative if , the subscripts indicating partial differentiation with respect to these variables. Using this show that the field  is conservative. Here .

2. Verify Stokes theorem for the vector  field  where the contour is a circle of radius R  in the xy plane centered at the origin. Take the surfaces to be (1) a disk (2) a hemisphere  and (3) a right circular cone radius R and height h.

3. Evaluate  over a circle of radius 2 whose centre is located at (0,2,2).

4. Show that the line integral of  along any closed contour is zero.

5. Find the contour integral of  along a triangle whose vertices are at the points (1,0,0), (0,1,0) and (0,0,1).