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#### KvGroOve

I was wondering about the relation between the Gradient, Electric Potential, and Electric Field. I know that if you take the Gradient of a scalar field, you get a resultant vector field in which the vector points in the direction of greatest increase when you take a infinitesimally small step.

1) What if there are multiple directions which all offer the greatest yet same amount of increase in the value of the scalar function? I believe that if it's a local minimum, the gradient of that specific spot is 0. But what if it's not a local minimum? How does the gradient operator handle that sort of situation? (I'm guessing that would mean a cross-section of the scalar field would trace out an inflection point).

2) The Electric Field can be given by

**E**=-∇φ

Thanks!