- #1
MrB3nn
- 16
- 0
1. The problem statement, all variables and givenknown data
Let r be a position vector from the origin (r=xi+yj+zk), whose magnitude is r, and let f(r) be a scalar function of r. Sketch the field lines of f(r)r
1 [tex]\nabla[/tex]x([tex]\nabla[/tex][tex]\Psi[/tex])=0
2 [tex]\nabla[/tex].([tex]\nabla[/tex]xv)=0
3 [tex]\nabla[/tex]x([tex]\nabla[/tex]xv)=[tex]\nabla[/tex]([tex]\nabla[/tex].v)-[tex]\nabla[/tex][tex]\^{}2[/tex]v
4 [tex]\nabla[/tex].([tex]\Psi[/tex]v)=[tex]\Psi[/tex][tex]\nabla[/tex].v+v.[tex]\nabla[/tex][tex]\Psi[/tex]
I can't get started on this question. I have no idea how you can draw a sketch of the field lines when the scalar function is unknown. My intuition says you should be able to use some of those identities but I need a push in the right direction. I hope someone can give me that.
Let r be a position vector from the origin (r=xi+yj+zk), whose magnitude is r, and let f(r) be a scalar function of r. Sketch the field lines of f(r)r
Homework Equations
1 [tex]\nabla[/tex]x([tex]\nabla[/tex][tex]\Psi[/tex])=0
2 [tex]\nabla[/tex].([tex]\nabla[/tex]xv)=0
3 [tex]\nabla[/tex]x([tex]\nabla[/tex]xv)=[tex]\nabla[/tex]([tex]\nabla[/tex].v)-[tex]\nabla[/tex][tex]\^{}2[/tex]v
4 [tex]\nabla[/tex].([tex]\Psi[/tex]v)=[tex]\Psi[/tex][tex]\nabla[/tex].v+v.[tex]\nabla[/tex][tex]\Psi[/tex]
The Attempt at a Solution
I can't get started on this question. I have no idea how you can draw a sketch of the field lines when the scalar function is unknown. My intuition says you should be able to use some of those identities but I need a push in the right direction. I hope someone can give me that.