Example 1 :
A particle moves counterclockwise along the curve from (1, 0) to a point P, under the action of the force
Prove that there are two possible locations of P such that the work done by is 1.
Point on ellipse is represented as
Work done in equal to 1
So, there are two value of i.e., two possible location of P such that the work done by is 1.
Example 2 :
Find the circulation of the field
around the curve C, where C is the intersection of the sphere and the plane z = 3. The orientation of the curve C is counterclockwise when viewed from above.
C is the curve of intersection of surfaces
For curve C, z = 3, dz = 0