# significance of curl and divergence of a vector field

A curl is in simplest words is the calculation of the circulation per unit area The physical significance of the curl of a vector field is the amount of "rotation" or angular momentum of the stuffing of given region of space. It happens in fluid mechanics and elasticity theory. It is also basic in the theory of electromagnetism. If the value of curl is zero then the field is said to be a non rotational field

The divergence actually measures how much the vector function is spreading out.

Divergence of a vector field A is a measure of how much a vector field converges to or diverges from a given point. In simple terms it is a measure of the outgoingness of a vector field. Divergence of a vector field is positive if the vector diverges or spread out from a given point called source- Divergence of a vector field is negative if the vector field converges at that point called sink. .If just as much of the vector field points in as out, the divergence will be approximately zero.

## Comments 30 comments

Are you a mathematician or engineer?

nice share brooooo

very helpful...thanks

i like your style.

do you have a simulation about curl

thanks dear

what do u mean by source and sink?

nice explanation. It made my concept clear

very useful thanks

very informative

Can u plz upload more details

insufficient data............

it has provided me a lot of information.

it is insufficient

insufficent

not enough

thanks

Sir you said that in electromagnetism is curl of a vector field is zero then it is non rotational field. Does this mean that the vector field do not rotate if the above condition is satisfied.

Thanks

sir plz tell me about significant of divergent of a vector field

thanks

thanks................... but what is mean by source and sink?

Thxxxx....i was so confused.....thx for help

Very nice

thanks.............

Thanks.....

it is really very much helpful

thanks.

can u add more data on it

Divergence (div) is “flux density”—the amount of flux entering

or leaving a point. Think of it as the rate of flux expansion

(positive divergence) or flux contraction (negative divergence).

If you measure flux in bananas (and c’mon, who doesn’t?), a

positive divergence means your location is a source of

bananas. You’ve hit the Donkey Kong jackpot.

Remember that by convention, flux is positive when it leaves a

closed surface. Imagine you were your normal self, and could

talk to points inside a vector field, asking what they saw:

If the point saw flux entering , he’d scream that everything

was closing in on him. This is a negative divergence, and

the point is capturing flux, like water going down a sink.

If the point saw flux leaving, he’d sniff his armpits and say

all flux was existing. This is a positive divergence, and the

point is a source of flux, like a hose.

So, divergence is just the net flux per unit volume, or “flux

density”, just like regular density is mass per unit volume (of

course, we don’t know about “negative” density). Imagine a tiny

cube—flux can be coming in on some sides, leaving on others,

and we combine all effects to figure out if the total flux is

entering or leaving.

The bigger the flux density (positive or negative), the stronger

the flux source or sink. A div of zero means there’s no net flux

change in side the region. In plain english:

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