How is electric field strength related to the electric potential gradient?

Here, we will find how electric field strength is related to the electric potential gradient. Before that, we will define the electric potential gradient.

Electric potential gradient

The electric potential gradient is the change of electric potential (V) with the change in distance(r).

Electric potential gradient = ΔV/Δr

The electric field strength can be defined as the negative of the electric potential gradient.
Electric field strength (E) =- ΔV/Δr

Hence the units V m−1.

Potential gradient from E-r graph (Electric Field strength vs distance graph)

Potential, potential gradient and
electric field in E-r graph
Potential, potential gradient and
electric field in E-r graph

The change in electric potential is equal to the area between two distances on the E−r graph.

ΔV= E Δr

How is electric field strength related to the electric potential gradient?
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