Electric field as a potential gradient

 

Electric potential

The electric potential or voltage is a scalar quantity that represents the potential energy per unit charge at a given point in an electric field. It is measured in volts. 

Electric field

The electric field, on the other hand, is a vector quantity that describes the force experienced by a charged particle at a given point in an electric field. It is measured in newtons per coulomb (N/C). 

The electric field can be described as the gradient of the electric potential. 

The gradient of a scalar field represents the direction and magnitude of the steepest increase in that field.

 In the case of the electric potential, the electric field can be determined by taking the negative gradient of the electric potential:

Electric field (E) = -∇V

Where E represents the electric field vector, ∇ is the gradient operator, and V represents the electric potential scalar field. 

This relationship suggests that the electric field is related to the rate of change of the electric potential. In other words, the electric field is a measure of how the electric potential changes as you move through space. A steeper change in the electric potential corresponds to a stronger electric field. In this sense, the electric field can be thought of as the potential gradient.