When the divergence and curl both are zero for vector field?

Curl and divergence are essentially “opposites” – essentially two “orthogonal” concepts. The entire field should be able to be broken into a curl component and a divergence component and if both are zero, the field must be zero.

What does it mean if the curl of a vector 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.

What is the name of a vector whose divergence is equal to zero?

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

What is divergence and curl of a vector field?

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 is the curl of F?

The curl of a vector field F, denoted by curl F, or ∇ × F, or rot F, at a point is defined in terms of its projection onto various lines through the point. If is any unit vector, the projection of the curl of F onto is defined to be the limiting value of a closed line integral in a plane orthogonal to.

What is the divergence of the vector field F?

The divergence of a vector field F = ,R> is defined as the partial derivative of P with respect to x plus the partial derivative of Q with respect to y plus the partial derivative of R with respect to z.

What does the zero value for the divergence of a vector field imply?

It means that if you take a very small volumetric space (assume a sphere for example) around a point where the divergence is zero, then the flux of the vector field into or out of that volume is zero. In other words, none of the arrows of the vector field will be piercing the sphere.