PG1995
Active Member
Hi
These days I'm learning about vector concepts of divergence, curl and gradient on a basic level.
Q1:
I was reading this Wikipedia article on the curl where it was written:
As the article says:
The curl gives us a direction of rotation and length/magnitude of that vector of rotation. What does the line in red mean in the quoted text above? Please help me with it. Thank you.
Q2:
Another article I was reading says:
I was thinking that in case of electric field the divergence is equivalent to magnitude of flux density. The magnitude of flux density is given as:
But I think I was wrong. Divergence = Flux/volume. The divergence is flux per unit volume but flux density is flux passing per unit area. What do you say? Please let me know. Thanks.
Regards
PG
These days I'm learning about vector concepts of divergence, curl and gradient on a basic level.
Q1:
I was reading this Wikipedia article on the curl where it was written:
Intuitive interpretation
Suppose the vector field describes the velocity field of a fluid flow (such as a large tank of liquid or gas) and a small ball is located within the fluid or gas (the centre of the ball being fixed at a certain point). If the ball has a rough surface, the fluid flowing past it will make it rotate. The rotation axis (oriented according to the right hand rule) points in the direction of the curl of the field at the centre of the ball, and the angular speed of the rotation is half the magnitude of the curl at this point.
As the article says:
In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a 3-dimensional vector field. At every point in the field, the curl of that field is represented by a vector. The attributes of this vector (length and direction) characterize the rotation at that point.
The curl gives us a direction of rotation and length/magnitude of that vector of rotation. What does the line in red mean in the quoted text above? Please help me with it. Thank you.
Q2:
Another article I was reading says:
In vector calculus, divergence is a vector operator that measures the magnitude of a vector field's source or sink at a given point, in terms of a signed scalar. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
I was thinking that in case of electric field the divergence is equivalent to magnitude of flux density. The magnitude of flux density is given as:
But I think I was wrong. Divergence = Flux/volume. The divergence is flux per unit volume but flux density is flux passing per unit area. What do you say? Please let me know. Thanks.
Regards
PG
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