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Mathematics 16 Online
OpenStudy (anonymous):

what does a conservative field means

OpenStudy (turingtest):

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

OpenStudy (turingtest):

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)

OpenStudy (anonymous):

thanks

OpenStudy (experimentx):

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

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