Does time varying voltage produce electric fields?

Question

We all know that if we have potential difference between two points in space, then there is an electric field between them but what if I had a region of space which is equipotential initially but has changing voltage due to some reason. So, there is an aspect of potential difference across  time, would this suggest a time varying electric field? or does only spatial variation in voltage produce  electric field.
More precisely speaking, Would time variations in voltage produce time varying electric field? if not, what makes spatial variations special? For example suppose I have a potential function of form $ V(x,y,z,t)$

Steeven · Answer

Voltage is a term for potential difference.
Two points being equipotential means that they have the same potential.

So, by this definition, the voltage between equipotential points is always zero.
In general, a voltage does not "cause" the electric field. Rather voltage is a feature of the field, or a measure of the field. With no field, there's no voltage because there's no tendency for charges to move.

Does time varying voltage produce electric fields?

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