What is the relation between electric potential and electric field?

Only a difference between potential and electricity can create an electric field. No electric field can exist regardless of how high the potential is. This is what happens in a hollow charged sphere. There is potential inside the sphere but there is no potential difference and therefore no field.

In general Electric field can be described as a negative space derivative potential.

Considering one dimensional case for simplicity,

E = -dV/dx

Or E= – (gradients of potential).

The (-) sign means that the field is directed from higher to lower potential.

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