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significance of curl and divergence of a vector field

Updated on January 24, 2011

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.

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    • profile image

      khushi 

      21 months ago

      Plz explain deeply source &sink

    • profile image

      naren 

      2 years ago

      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:

    • profile image

      aswin 

      2 years ago

      thanks.

      can u add more data on it

    • profile image

      Neha 

      3 years ago

      Thanks.....

      it is really very much helpful

    • profile image

      deepakshi 

      3 years ago

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

    • profile image

      sameer 

      3 years ago

      Very nice

    • profile image

      pooja bansal 

      3 years ago

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

    • profile image

      divya 

      3 years ago

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

    • profile image

      mahi 

      4 years ago

      thanks

    • profile image

      hassanjalil 

      4 years ago

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

    • profile image

      amit 

      4 years ago

      Thanks

    • profile image

      javed 

      4 years ago

      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.

    • profile image

      shakir 

      4 years ago

      thanks

    • profile image

      pinky 

      4 years ago

      not enough

    • profile image

      abeeha rao 

      4 years ago

      insufficent

    • profile image

      abeeha 

      4 years ago

      it is insufficient

    • profile image

      hafeez ahmad 

      4 years ago

      it has provided me a lot of information.

    • profile image

      ahsan.ch 

      4 years ago

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

    • profile image

      waqar ahmad 

      4 years ago

      Can u plz upload more details

    • profile image

      sidra 

      4 years ago

      very informative

    • profile image

      mohsin liskani 

      4 years ago

      very useful thanks

    • profile image

      rankanidhi pradhan 

      4 years ago

      nice explanation. It made my concept clear

    • profile image

      Javeria anis 

      5 years ago

      what do u mean by source and sink?

    • profile image

      ricky 

      5 years ago

      thanks dear

    • profile image

      tamer 

      5 years ago

      do you have a simulation about curl

    • profile image

      nb rana 

      6 years ago

      i like your style.

    • profile image

      ujjwal 

      6 years ago

      very helpful...thanks

    • profile image

      rajeev 

      7 years ago

      nice share brooooo

    • profile imageAUTHOR

      usman0786 

      7 years ago

      I'm Student

    • Denise Handlon profile image

      Denise Handlon 

      7 years ago from North Carolina

      Are you a mathematician or engineer?

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