The physical significance of curl of a vector

[chickoos]

Hi,

Does anybody knows the physical significance of curl of a vector?

 

[maxwelleb]

Re: Electromagnetics

whenever at any point in the space you have changing magnetic field you have curl of the electric field; you get generally non conservative electric potentials; so going a loop in space makes a net change in energy;

 

[Mr.Cool]

Re: Electromagnetics

The physical significance of the curl of a vector field is the amount of "rotation" or angular momentum of the contents of given region of space.

h**p://mathworld.wolfram.com/Curl.html

Mr.Cool

 

[nijirazdan]

Electromagnetics

curl is a wonderful concept.its what accounts for em wave propagation.imagine a waterpipe closed at one end.now when the liquid flowing in the wire encounters this closed end,it circulates in the pipe this is curl effect.for further details u can always look into feynman's physics book(vol.2 on electromagnetics)

 

[nijirazdan]

Re: Electromagnetics

just like if the end of a pipe is closed at one end,the water circulates in the pipe this is known as curl

 

[Mr.Cool]

Electromagnetics

nijirazdan i like your analogy.

here is the kicker.. your analogy makes it very clear that the energy associated with the curl vector (its moving, so must have energy) is entirely contained WITHIN the pipe.. the water can't leak out of the metal pipe after all..

mathematically speaking, this would be like integrating about the closed path.. where one looks at what is within the border of the integral.

here is the assumption with this analogy and math:
that there is NO energy outside the pipe wall, or if you give the benefit of the doubt, there is no "practically usable" energy outside the wall of the pipe.

what then is the significance of the Heaviside Component?

food for thought...

 

[suvendu]

Re: Electromagnetics

The significance of curl is "rotation".if curl is zero then field is conservative.

 

[antaresv]

Re: Electromagnetics

The significance of curl is "rotation".if curl is zero then field is conservative.

Respectfully, rotation can be misleading. The essence of the curl is transverse change. In a 3D vectorial field, if your component in one direction has a variation in the transverse direction, it will induce a curl.

For example, if your x-component of the vector varies as you move along the y or z direction, it will induce a curl. For the nice water pipe analogy mentioned about, the curl is induced at the boundary of the water flow (the transition from a point with flowing water just inside the pipe to just outside the pipe where there is no flowing water).

 

[aersoy]

Re: Electromagnetics

it is the maximun net cirulation as the area about the point goes to zero.

 

[neils_arm_strong]

Electromagnetics

curl of a vector gives us the value of twice the angular velocity.