Is curl of a scalar field possible?

In a scalar field there can be no difference, so the curl of the gradient is zero.

Can we find divergence of scalar field?

In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field’s source at each point. The divergence of the velocity field in that region would thus have a positive value.

Can we define the divergence of a scalar function?

Key Concepts. The divergence of a vector field is a scalar function. Divergence measures the “outflowing-ness” of a vector field. If v is the velocity field of a fluid, then the divergence of v at a point is the outflow of the fluid less the inflow at the point.

Why don’t we use the curl and divergence operations for scalar fields?

The curl and divergence are vector operations, where [math]\ abla[/math] is treated like a vector and applied through the cross and dot product respectively. Naturally, these can only apply to vectors, and do not make sense with scalars. Physically, it also doesn’t make sense to apply curl and divergence of a scalar field.

What is the difference between Curl and divergence?

In addition to defining curl and divergence, we look at some physical interpretations of them, and show their relationship to conservative and source-free vector fields. Divergence is an operation on a vector field that tells us how the field behaves toward or away from a point.

What is a curl-free vector field?

Consider first a curl-free vector field, which can be imagined as a sea of flowing fluids, with sources (such as a tap or waterfall) at locations with positive divergence, and sinks (such as drains or siphons) at places with negative divergence. However, this does not make sense for scalar fields, which are directionless.

Does the divergence of a scalar field make sense?

Clearly, this makes no sense. If you use the common, intuitive fluid metaphor for fields, you can also visualise why the divergence of a scalar field doesn’t make sense.