Can divergence and curl both be zero?

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 happens when divergence 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.

What is the nature of the field if the divergence is zero and curl is also zero?

Explanation: Since the vector field does not diverge (moves in a straight path), the divergence is zero. Also, the path does not possess any curls, so the field is irrotational.

When curl is zero?

The curl of E is identically zero. When the gradient of a scalar field is flat( constant)i.e; slope is zero , then the curl of the gradient of this scalar field is zero. When the integration of a vector over a closed loop enclosing an open finite area is zero , the curl is zero.

What is the meaning of 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.

Why is the curl of an electric field zero?

The curl of a electric field is zero, i.e. ∇ → × E → = 0 Because, no set of charge, regardless of their size and position could ever produce a field whose curl is not zero.

How to calculate divergence?

Calculating divergence as a sum of all the terms: D i v A → = (− 2 x sin (x 2) + x cos (x y) + 0)

Is the divergence of a magnetic field zero?

Divergence of magnetic field is zero everywhere because if it is not it would mean that a monopole is there since field can converge to or diverge from monopole. But magnetic monopole doesn’t exist in space. So its divergence is zero everywhere.