## Saturday, 26 April 2014

### CURL PART 2: THE SIGNIFICANCE OF i,j & k TERMS

|||| Quick highlights about the basics of Curl from the previous post on CURL HERE.

1] Curl is a measure of how much an object can make you rotate or spin.
2] It varies as you move away from the centre (source) and so we have the partial derivatives along the x, y and z axises.
3] The 'X' sign in Curl is an indicator that the effect of Curl is maximum when the object is kept perpendicular to the flow of the continously curling field.

NOW ABOUT THE SIGNIFICANCE OF THE  i, j and k TERMS IN THE EQUATIONS OF THE CURL.

|||| The i term or i plane lets say indicates revolution about the horizontal plane. That means the object is experiencing a force which is making it revolve in the horizontal plane (much like a planet revolving around the sun or a satellite moving along the equator of the earth)

|||| So the j term or j plane indicates revolution about the vertical plane. That means the object is experiencing a force which is making it revolve slightly vertically also. Imagine a satellite moving along an inclined orbit around the earth.
|||| The k term or k plane means now the object is rotating about its own axis also. So now our satellite is moving along an inclined path ( i.e slightly horizontally and slightly vertically simultaneously) and at the same time rotating about its own axis.

So........Basically

|| Only the i term means only  horizontal curl or horizontal revolution.
|| Only the j term means only  vertical curl or vertical revolution.
|| An i + j term would mean....horizontal as well as vertical revolution  taking place simultaneously (inclined revolution).
|| And and i + j + k term would mean inclined revolution path plus rotation of the object about its axis.
|| Only k term might mean that the object is rotating about its axis,......but is not revolving about anything

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I hardly understood Math in school. In fact was on the verge of dropping the subject I loved the most because as much as I loved the theory of it, I could not understand the math involved in it. However I loved the subject too much to be able to live without. Hopelessly, I was continuing my love-affair with it.

Then one day....a miracle happened,....while applying a certain formula again and again.....I came to know its significance. Slowly and steadily....other equations also started clicking. I got to see a strong relationship between Maths and the Physics it was pointing towards. They both were the same. Maths was just an easy language to express a physical phenomenon. And a bit more to that in the sense that it could even predict the behaviour of a certain physical phenomenon. Equations now as if came to life.

Every equation now had as if something to say. A burning urge to share these things with the world aflamed within me. So that no one has to give up the subject that he or she loves the most.
The book on visualizing maths thus got written as a sprout of inspiration. The blog followed. Both these are dedicated to you and all such similar minds searching for answers.

Visualizing Math & Physics is a blog dedicated to you and all such similar minds searching for answers.

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binnoypanicker@gmail.com

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