Question

what does a conservative field means

Answer 1

a vector field \(\vec F=\langle p(x,y,z),q(x,y,z),r(x,y,z)\rangle\)is conservative if it is the gradient of some function \(f(x,y,z)\)

that is, if \[\vec F=\nabla f(x,y,z)\]then \(\vec F\) is a conservative vector field

Answer 2

for example, in physics if we have a function to describe the electric potential in 3-space \(V(x,y,z)\) then the electric field vector function is given by \[\vec E=-\nabla V\]which tells us that electric fields are conservative (at least when the potential function is not changing)

Answer 3

thanks

Answer 4

Ir-rotational fields are Conservative fields
\[ \nabla \times \vec E = 0\]