Why is the electric field in the direction in which the potential decrease is steepest?

Question

My question is, why is it necessary for the potential decrease to be steepest? We could simply say that the direction of the electric field is in the direction where the potential decreases.

Yejus · Answer

The definition of the electric field is the negative gradient of the electric potential:
$$mathbf{E= -nabla} V.$$ Geometrically, the gradient of a scalar function is the direction in which it is changing the most. Put the two ideas together, and you have your answer.

Why is the electric field in the direction in which the potential decrease is steepest?

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