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**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.

**Solution :**

Point on ellipse is represented as

Work done in equal to 1

So,

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.

**Solution :**

*C* is the curve of intersection of surfaces

So,

For curve *C*, *z* = 3, *dz* = 0

Let

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