Just clarify; Not a homework problem

[neelakash]

Homework Statement

We know cyclic integral F(r).dl=0 => curl F(r)=0 and F(r) is a conservative vector field.
What if the vector field is NOT a function of r(x,y,z)?Suppose,F is a function of velocity or time...i.e. F=F(v) or F=F(t).Say we do not know v=v(r) or t=t(r).In that case will the field be at all consevative?

Is magnetic force (Lorentz force F=v x B ) a function of velocity?

Homework Equations

The Attempt at a Solution

 

[Hootenanny]

Homework Statement

We know cyclic integral F(r).dl=0 => curl F(r)=0 and F(r) is a conservative vector field.
What if the vector field is NOT a function of r(x,y,z)?Suppose,F is a function of velocity or time...i.e. F=F(v) or F=F(t).Say we do not know v=v(r) or t=t(r).In that case will the field be at all consevative?

You might want to check out http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html#cfor

Is magnetic force (Lorentz force F=v x B ) a function of velocity?

Yes.

 

[neelakash]

So,conservative vector field is only function of r,always...Right?The purpose of the question was to know another way to see that lorentz force is not conservative.Since curl E= -(del B/del t)...that is a common way to see it.
But if you know that this force is a function of velocity and for a field to be conservative,it is to be a function of position only,atleast qualitatively you know that the curl cannot be zero,nor the closed loop line integral is going to be zero.

Often there are cases where we use something (which we do not understand clearly) to prove another...Like this.I,perhaps, do not understand NOW why magnetic force is a function of velocity...Is this velocity is the velocity of the source charge or the test charge?