What is divergence?

Question

What is it's physical significance? What changes could we see if Divergence of something which is usually = 0 (Say Magneic field B) is = const.?

Answer 1

The divergence of a field is a measure of how much of that field has "escaped."

For example, a lone positive electric charge inside a box would have field lines that extend out from it everywhere and continue forever. These lines have "escaped" from the box. They never return to the box. If you placed a negative electric charge within the box, then those field lines would start to curve around and terminate at the negative charge. That is, you will have placed an "electric dipole" within the box.

There are no "magnetic monpoles." That is, there are no single "north charges" or "south charges." Charges always come in pairs. Every "north" always comes with a "south." Thus, when you have an object generating a MAGNETIC FIELD within a box, you can be 100% certain that every field line EXITING the box will curve around and terminate within the box. Each field line MUST return to where it started. (I am using a "box" to help with visualization; this box may be made infinitely small)

This is, in fact, why it is impossible to attenuate (or "block") magnetic fields in the same way that you can with electric fields. If magnetic fields could be blocked, you could conceivably build a box that would prevent a field line from returning to its source. Since the divergence of a magnetic field is 0, this is not possible. Thus, the best you can do is put a highly permeable material around the object that you want to "shield." MOST of the field lines will then travel within the materials in the highly permeable skin of box because it's the path of least "resistance" (there are such things as "magnetic circuits" and they have something that is analogous to "resistance"). This will prevent many of the lines from entering the inside of the box. However, after traveling through the skin of the box, those lines will regroup and continue back to their original source. They must because div B = 0.

Answer 2

In vector calculus, the divergence is an operator that measures a vector field's tendency to originate from or converge upon a given point. For instance, for a vector field that denotes the velocity of air expanding as it is heated, the divergence of the velocity field would have a positive value because the air is expanding. Conversely, if the air is cooling and contracting, the divergence would be negative.

A vector field which has zero divergence everywhere is called solenoidal.

You could view Physical interpretation at the link below...

Answer 3

Divergence in the case of a Magnetic Field is always ZERO, because magnetic fields always occur in nature as a dipole, i.e. north and south magnetic poles.

If the divergence of a magnetic field is not zero, but equal some constant, then we would have a "Magnetic Monopole", that is a magnetic north or south pole without the other to terminate the magnetic fields.

If you look at the differential equation for an electric field, whose divergence is non-zero, you'll see that electric fields always terminate at either a positive or a negative charge, but usually there is no electric dipole, requiring the electric fields to terminate like a magnetic field of a magnetic dipole. So basically all electric charges like the electron or proton are "electric monopoles".

Answer 4

What Is Divergence

Answer 5

Let x, y, z be a system of Cartesian coordinates on a 3-dimensional Euclidean space, and let i, j, k be the corresponding basis of unit vectors.

The divergence of a continuously differentiable vector field F = F1 i + F2 j + F3 k is defined to be the scalar-valued function:


Although expressed in terms of coordinates, the result is invariant under orthogonal transformations, as the physical interpretation suggests.

The common notation for the divergence ∇·F is a convenient mnemonic, where the dot denotes something just reminiscent of the dot product: take the components of ∇ (see del), apply them to the components of F, and sum the results.

Answer 6

di·ver·gence (dĭ-vûr'jəns, dī-)
n.

The act of diverging.
The state of being divergent.
The degree by which things diverge.
Physiology. A turning of both eyes outward from a common point or of one eye when the other is fixed.
Departure from a norm; deviation.
Difference, as of opinion. See synonyms at deviation, difference.
Biology. The evolutionary tendency or process by which animals or plants that are descended from a common ancestor evolve into different forms when living under different conditions.
Mathematics. The property or manner of diverging; failure to approach a limit.
A meteorological condition characterized by the uniform expansion in volume of a mass of air over a region, usually accompanied by fair dry weather.

Answer 7

Divergence is the opposite Convergence
If you have an indefinite serie a(n) and it don't go to a certain value for n going to infinity the Serie is sayed to be divergent, On the other hand if it has a certain value it goes to it is convergent

Ex. a(n)= 1/n for n =1,2,........
its convergent against 0 for n going to infinity
ex a(n)=n for n=1.2.3......
is divergent because it has no limit value

Answer 8

The word 'divergence' means going away in different directions from a common path or point.

Answer 9

Watching the stars satisfies my soul
thinking of him makes me feel so cold
The fancy cars and the restaurants
you're just so fond of the man
Sometimes I wonder if you are blind
can't you see, he's got dirt on his mind
Chorus:
I'm not an actor I'm not a star
and I don't even have my own car...

Answer 10

divergence is simply the DOT OR SCALAR PRODUCT OF ANY VECTOR WITH DEL OPERATOR.