Conservative force fields and E pot?
First of all, what is the inverted triangle? Does gradient simply mean that in a conventional force field there is an Ep gradient depending on position? How would this contrast with a normal force field?
And Ep is, for example, m*g*h. How can you then take the partial derivative with respect to x, y, and z if the variables don't appear there?
Okay, I somehow believe that you have to differentiate, for example, the x component of r, but I can't imagine it being practical. Does anyone have an example using simple numbers to show how to calculate this?
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The twisted triangle is the Nabla operator. It is used as a vector whose components are partial discharge operators.
The potential energy is a scalar size, the force a vector. The Nabla operator ensures the conversion/configures the connection.
In the vector r (x,y,z) already occurs, in spherical coordinates r=root is from (x2+y2+z2). For simplicity, we set the coordinate system so that r=z=h, the potential energy is m*g*z.
If you conduct this partially to x,y and z and minus sign before, then you get the force vector (0.0,-mg). The third component is the well-known F=m*g and the minus sign says the force acts downward. No force acts in the lateral directions x and y.