Electric field between two points

Question

We all know that electric field goes from higher potential to lower potential.
And $$dV=-\vec{E}.\vec{dr}$$

Now assume two different points in space (separated by some distance $d$).

Potential at these two points is known ($V_1>V_2$).

Can we comment on the electric field strength between these two points? We only know the potential of points. (there is no information regarding charge system and its geometry)

In general, when someone tells that this is at higher potential and this is at lower potential (with values), can we find electric field with this information?

If yes the how and if no then why ?

Answer 1

We all know that electric field goes from higher potential to lower potential.

The electric field sometimes goes in loops. That is the case when the electric field is induced by a time-varying magnetic field.

In general, when someone tells that this is at higher potential and this is at lower potential (with values), can we find electric field with this information?

In general, no. The electric field is created by a) charge distribution, and b) time varying magnetic fields. Since we know nothing about those two factors, we cannot deduce the field given only the potential at two points. There might be a straight field line between the points. There might be a curved field line between the points. The two points might not be connected by a field line at all. We just don't have sufficient information.