Question

Consider the vector field } = (x2 - y2 + x) i - (2xy + y)used to move a particle from origin to the point (1,1) along y2 = x.

Answer 1

Answer:

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Step-by-step explanation:

The force acting F(x,y)=x

2

i

^

+y

2

j

^

Thus we get F

x

=x

2

and F

y

=y

2

Now

∂x

∂F

y

=

∂x

∂y

2

=0

Similarly,

∂y

∂F

x

=

∂y

∂x

2

=0

For the force to be a conservative force,

∂x

∂F

y

−

∂y

∂F

x

=0

⟹ F(x,y) is a conservative force.

Work done by a conservative force is zero for a closed loop.

⟹ Work done by force F(x,y) around the path given is zero.