What if the divergence of a vector field is zero?

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.

When the divergence of a vector is zero it is said to be solenoidal divergent free?

Curl (v). Explanation: When the divergence of a vector is zero, it is said to be solenoidal /divergent-free. Explanation: By Maxwell’s equation, the magnetic field intensity is solenoidal due to the absence of magnetic monopoles.

What is the condition for a vector field solenoidal?

If there is no gain or loss of fluid anywhere then div F = 0. Such a vector field is said to be solenoidal.

What does divergence being 0 mean?

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.

When the divergence and curl both are zero for a 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.

Which of the following identities is always zero for static fields?

The curl of gradient of
5. Which of the following identities is always zero for static fields? Explanation: The curl of gradient of a vector is always zero. This is because the gradient of V is E and the curl of E is zero for static fields.

What is Solenoidal in vector?

In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field) is a vector field v with divergence zero at all points in the field: A common way of expressing this property is to say that the field has no sources or sinks.

What is a Solenoidal?

A solenoid is a device comprised of a coil of wire, the housing and a moveable plunger (armature). When an electrical current is introduced, a magnetic field forms around the coil which draws the plunger in. More simply, a solenoid converts electrical energy into mechanical work.

What do you mean by Solenoidal vector?

What happens when the curl is zero?

If the curl is zero, then the leaf doesn’t rotate as it moves through the fluid. Note that the curl of a vector field is a vector field, in contrast to divergence.

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.

Why is the divergence of a vector field always zero?

The curl of any and all vector fields always results in a solenoidal vector field. The surface integral of a solenoidal field across any closed surface is equal to zero. The divergence of every solenoidal vector field is equal to zero. The divergence of a vector field is zero only if it is solenoidal.

Why do the lines of a vector field follow a path?

Because there are only two possibilities. The lines of a vector field either terminate, (as with the electric field, at electric charges,) or they follow closed paths, (as with the magnetic field, which encircles electric currents, owing to the lack of magnetic monopoles.)

What is a vector field in statistics?

A Vector field is a field where a Vector is defined at each point. For convenience sake, most fields we start with are smooth and continuous i.e if we move from a point to a neighbouring point, we have another vector noting that Zero Vector is also a Valid Vector. There is no discontinuity or holes.

Is the exterior derivative of a derivative always null?

But this result is a form of a more general theorem that is formulated in term of exterior derivatives and says that: the exterior derivative of an exterior derivative is always null. In this case E is the exterior derivative of F and div ( E) is the exterior derivative of E.