Question

What is conservative field ? Show that curl of
such a field is zero.​

Answer 1

Answer:

This condition is based on the fact that a vector field F is conservative if and only if F=∇f for some potential function. We can calculate that the curl of a gradient is zero, curl∇f=0, for any twice continuously differentiable f:R3→R. Therefore, if F is conservative, then its curl must be zero, as curlF=curl∇f=0.

Answer 2

Answer:

A conservative vector field in vector calculus is a vector field that is the gradient of some function. The line integral in conservative vector fields is path independent; choosing any path between two points does not change the value of the line integral.

Explanation:

Curl of such a field is zero:

This condition is based on the fact that for some potential function, a vector field F is conservative if and only if F=∇f, curl∇f=0, For any twice continuously differentiable f:R3→R we can calculate that the curl of a gradient is zero, curl∇f=0. As a result, if F is conservative, its curl must be zero, because curlF=curl∇f=0.

Because a conservative vector field is defined as the gradient of a function, which is commonly referred to as the "scalar potential." And we can derive vector identities from them. The leaf does not rotate as it moves through the fluid if the curl is zero. In contrast to divergence, the curl of a vector field is a vector field. As a result, this matrix can be used to help remember the curl formula.