Can a vector field have divergence and curl?

The divergence and curl of a vector field are two vector operators whose basic properties can be understood geometrically by viewing a vector field as the flow of a fluid or gas. The curl of a vector field captures the idea of how a fluid may rotate. Imagine that the below vector field F represents fluid flow.

What will be the nature of the field if its divergence and curl both are zero?

The divergence of curl of a vector is zero. State True or False. Curl is defined as the angular velocity at every point of the vector field….

Q.	Identify the nature of the field, if the divergence is zero and curl is also zero.
B.	divergent, rotational
C.	solenoidal, irrotational
D.	divergent, rotational

When divergence of a vector is zero that vector can be represented as?

solenoidal
A vector field with zero divergence everywhere is called solenoidal – in which case any closed surface has no net flux across it.

What does it mean if the curl of a vector field is zero?

Curl indicates “rotational” or “irrotational” character. Zero curl means there is no rotational aspect to vector field. Non-zero means there is a rotational aspect.

Is divergence of curl zero?

In words, this says that the divergence of the curl is zero. That is, the curl of a gradient is the zero vector. Recalling that gradients are conservative vector fields, this says that the curl of a conservative vector field is the zero vector.

What is divergence and curl of a vector?

Roughly speaking, divergence measures the tendency of the fluid to collect or disperse at a point, and curl measures the tendency of the fluid to swirl around the point. Divergence is a scalar, that is, a single number, while curl is itself a vector.

Is curl scalar or vector?

In vector calculus, the curl is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation.

Why is the divergence of a curl zero?

The stokes theorem gives the integral of the curl of a vector field on a surface in therms of the integral of the vector field on the boundary that encircles that surface. So, the divergence of the curl being zero means that the boundary has no boundary.

What is curl vector field?

The curl of a vector field provides a. measure of the amount of rotation of the vector field at a point. In general, the curl of any vector point function gives the measure of angular velocity at any. point of the vector field. The curl operation is restricted to how the field changes as one move.

Does there exist a conservative field with non zero curl?

Without additional conditions on the vector field, the converse may not be true, so we cannot conclude that F is conservative just from its curl being zero. There are path-dependent vector fields with zero curl. On the other hand, we can conclude that if the curl of F is non-zero, then F must be path-dependent.

Is curl a vector or scalar?

In vector calculus, the curl is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space.

What does it mean if divergence is zero?

zero divergence means that the amount going into a region equals the amount coming out. in other words, nothing is lost. so for example the divergence of the density of a fluid is (usually) zero because you can’t (unless there’s a “source” or “sink”) create (or destroy) mass.