Question

What does the ‘non-zero nature of curl of magnetic field induction’ signify?​

Answer 1

Answer:

Your intuition about the meaning of the divergence operator is wrong. We can interpret this by saying there's no net flow of magnetic field across any closed surface. This makes sense because magnetic field lines always come in complete loops, rather than starting or ending at a point.

Answer 2

Explanation:

let me start by stating that the curl of the electric field is not always zero; the general law for the curl of the electric field is one of the Maxwell’s equations which states that:

∇×E⃗ =−∂B⃗ ∂t

It is only when the magnetic field is either zero or constant is it true that the curl of electric field is zero.

To see as to why the curl of electric field is zero; let’s look at Coulomb’s law- which has the key feature that F∼1/r2; this looks a lot like Newtonian gravity and in fact any force which depends only on the distance is called a central force: the reason is that the interaction between objects under such a force is along the line joining them.

One of the properties of the central force is that they are conservation in nature, meaning the work done under such a force would depend only on the end points. This amounts to writing the force as a gradient of some potential, and then by the familiar identity that the curl of a gradient is zero you can see why the curl of the electric field vanishes.