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Physics
Classical Physics
Electromagnetism
Gradient, Electric Potential, and Electric Field
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[QUOTE="Orodruin, post: 5837838, member: 510075"] This does not happen. As long as the function can be well approximated by a linear function, there will always be a unique direction of fastest increase. If the gradient is zero, then the linear part of the change in the function value vanishes and the change in the function is of second order or higher in the displacement. It is a linear approximation of the function near the point so yes, it is the direction of fastest decrease in potential. Again, this presupposes that the function can be approximated by a linear function near the point (think a plane in 3D). If this is not the case the function is not differentiable. [/QUOTE]
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Forums
Physics
Classical Physics
Electromagnetism
Gradient, Electric Potential, and Electric Field
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