Question

Using Stokes Theorem, calculate the work required to move a particle around the contour defined by the intersection of the plane x= 5 and a closed, right, circular cylinder, centered on the z-axis with a radius of 3 that extends from z=−1 to 3 , if the force acting on that particle is as follows:

Fˉ= 2y²a + 4x³ay + 4yaz

Answer 1

To calculate the work required to move a particle around the contour defined by the intersection of the plane x= 5 and a closed, right, circular cylinder, we can use Stoke's Theorem.

Step-by-step explanation:

To calculate the work required to move a particle around the contour defined by the intersection of the plane x= 5 and a closed, right, circular cylinder, we can use Stoke's Theorem. First, we need to find the circulation of the force field around the contour. The force acting on the particle is given by F = 2y²a + 4x³ay + 4yaz.

The circulation is obtained by taking the dot product of the force with the tangential vector of the contour, which is T = ∇×r. We evaluate this dot product and integrate it over the contour to find the work required to move the particle around the contour.