The potential gradient links field strength to potential

Electric Fields & Potential — AQA A-Level Physics

Key Definition

Potential gradient — The rate of change of electric potential with respect to displacement in the direction of the field.

E = -\frac{\Delta V}{\Delta r}

$E$: electric field strengthThe force per unit positive chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). at a point in an electric field. Measured in N C⁻¹ or V m⁻¹. (V m^-1)
$DeltaV$: potential differenceThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). between two points (V)
$Deltar$: displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). in the direction of the field (m)

The negative sign indicates that E points in the direction of decreasing potential.
The gradient of a V-r graph at any point equals the electric field strengthThe force per unit positive chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). at a point in an electric field. Measured in N C⁻¹ or V m⁻¹. E at that point.
The area under an E-r graph between two points equals the potential differenceThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). between those points.
The V-r graph follows a 1/r relationship. The E-r graph follows a 1/$r^{2}$ relationship. The E-r curve is steeper.