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Mr Genius
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Why the curl of a conservative force field is zero everywhere?
Yesrobphy said:Can your conservative force be written as a gradient of a scalar field?
ummm this didn't helpOrodruin said:Because a field being conservative is equivalent to having zero curl. This should be derived in any basic text on vector analysis.
Now take the curl of that gradient.Mr Genius said:Yes
Ummm I'm looking for the physical meaning and significant of thisrobphy said:Now take the curl of that gradient.
I am saying you should find this explained in detail in any basic textbook. This makes me wonder what effort you spent on trying to find the answer before posting.Mr Genius said:ummm this didn't help
This is mentioned without any illustration in my physics book, and there is nothing called conservative force in mathematics to explain it in a math bookOrodruin said:I am saying you should find this explained in detail in any basic textbook. This makes me wonder what effort you spent on trying to find the answer before posting.
Perhaps not conservative force, but certainly conservative vector field. A conservative force field is just a conservative vector field describing a force.Mr Genius said:there is nothing called conservative force in mathematics to explain it in a math book
Well, if u can find that then please send me a linkOrodruin said:Perhaps not conservative force, but certainly conservative vector field. A conservative force field is just a conservative vector field describing a force.
Loosely speaking, non-zero curl means that the vector field "goes in circles" somewhere, that you can follow the vector at one point to another and eventually get back where you started without ever going against the direction of the vector field at some point. For example, if the vector field were describing the current at the surface of a body of water, non-zero curl would mean that there was a whirlpool somewhere, so you could go around and around in circles without ever having to go against the current.Mr Genius said:Ummm I'm looking for the physical meaning and significant of this
http://lmgtfy.com/?q=conservative+vector+fieldMr Genius said:Well, if u can find that then please send me a link
Ohhthanks for ur time and that sweet linkOrodruin said:
Curl of conservative force is a mathematical concept used to describe the rotation or circulation of a vector field. It is a measure of how much a vector field "curls" or rotates around a given point.
The curl of a vector field is calculated using partial derivatives. In three-dimensional space, it can be represented by a vector with three components, each of which is calculated using a partial derivative with respect to one of the three dimensions.
A non-zero curl of conservative force indicates that the vector field is not irrotational, meaning that it has rotation or circulation around at least one point. This implies that the vector field is not conservative, as it cannot be described by a scalar potential function.
In physics, the curl of a conservative force is related to the rotational motion of a physical system. It is used to calculate the angular momentum and torque of a system, and is a key concept in the study of fluid dynamics and electromagnetism.
The concept of curl of conservative force is used in a variety of real-world applications, such as analyzing fluid flow in engineering and understanding the movement of air in weather patterns. It is also used in the calculation of magnetic fields and in the study of rotational motion in physics and astronomy.