In vector analysis, the gradient operator transforms a scalar field into a vector field. If this particular scalar happens to be an energy potential then the gradient changes the energy function into vector function of a force. Furthermore, if the energy as function of distance is plotted against the distance then a particular slope of this plot gives the magnitude of the force. Moreover, the sign of the slope indicates whether the force is repulsive or attractive. Depending on the coordinate system and its transformations, the slope can vary both magnitude and sign such that it can be repulsive in one system and attractive in another.


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