Why is the curl of a conservative vector field equal to zero?

Because by definition the line integral of a conservative vector field is path independent so there is a function f whose exterior derivative is the gradient df. Than the curl is *d(df)=0 because the boundary of the boundary is zero, dd=0.

What is the value of curl of a position vector?

How the curl of position vector is zero.

Why is the conservative force zero?

The total work done by a conservative force is independent of the path resulting in a given displacement and is equal to zero when the path is a closed loop. Nonconservative forces, such as friction, that depend on other factors, such as velocity, are dissipative, and no potential energy can be defined for them.

What does it mean if the curl of a vector is zero?

If curl of a vector field is non zero then it mean it is a rotating type of field (means the line representing the direction vector field form a closed loop)example for magnetic field and non conservative electric field. The curl of a vector is zero when the vector can be written as the gradient of a scalar.

Why is the curl of an electric field zero?

If you go to the definition of the curl you will see that this is a collection of partial derivatives with respect to position. So to claim that the curl is zero is to claim that the velocity is independent of the particles position, ie. it is assumed that there are no other fields present, be it gravitaional or electrical.

What is a curl in physics?

The curl is a differential operator that takes one three-dimensional vector field and spits out another three-dimensional vector field. To get a sense for what the curl means, imagine that we have a vector field that represents the velocity of a fluid.

Does zero curl imply zero circulation?

To finish let me mention that a vanishing curl (even for a position only dependent force) does not implies, in general, that the force is conservative. Those things are equivalent only when the space is simply connected. When this is not the case, the Stokes and Green theorems fail and zero curl does not imply zero circulation.