The potential gradient is equal to the rate of change of electric potential with respect to distance in a particular direction. Mathematically, it is represented as the derivative of the potential VVV with respect to position xxx, given by
potential gradient=dVdx\text{potential gradient}=\frac{dV}{dx}potential gradient=dxdV
This quantity describes how the electric potential changes spatially and has units of volts per meter (V/m). Importantly, the electric field E\mathbf{E}E is equal to the negative of the potential gradient:
E=−∇V\mathbf{E}=-\nabla VE=−∇V
This means the electric field points in the direction of steepest potential decrease with magnitude equal to the magnitude of the potential gradient. Thus, the potential gradient gives the spatial rate of change of potential, while the electric field is the vector field associated with that change but in the opposite direction.
