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- Thread starter redredred
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Mute

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Now, what underlies this mathematically is the concept of vector fields. The force of gravity and the electrostatic attraction between charged particles are examples of vector fields. A conservative vector field is one with an associated potential function (the vector field is the gradient of the potential function). If you perform a line integral between two points of a conservative vector field, the value of the integral depends only on the value of the potential function at the two points, not on the path between them, just like the Work done by a conservative force.

So, unless you have a different context for "potential function", gravitational potential is really just an example of a potential function and the gravitational force is really just an example of a vector field.

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Mute

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(*There are of course always caveats, one being that if the domain your vector field is defined on has a hole in it, for example, the theorem doesn't apply)

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