Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. F = 3yi + yj+zk C: counterclockwise path around the boundary of the ellipse x2/4+y2/64=1

= 12π

Step-by-step explanation:

The field F is given by:

     (1)

The curve C is the ellipse:

In order to calculate the circulation of F around the curve C, you first find the parametric equation for the given ellipse.

The general form of an ellipse equation is:

The parametric equation is:

     (2)

The Stokes's theorem is given by the following identity:

The path integral is also:

     (3)

For F(r(t)) and dr(t) you obtain:

Next, in the equation (3) you obtain:

The circulation of the field around C is 12π

30005

yes ok                                            

answer:   c ?

step-by-step explanation: