Potential Gradient

Potential gradient links two central ideas of electrostatics — electric potential and electric field. It tells us how fast potential changes as we move through space, and this rate of change is directly connected to the strength of the electric field.

Analogy: Imagine walking down a hill. The steeper the slope, the faster your height (potential energy) drops per step. Similarly, a steep "potential slope" in an electric field means a strong electric field; a gentle slope means a weak one.

Potential Gradient is the rate of change of electric potential (V) with respect to distance (r) in the direction of the electric field.

• SI unit: V/m (vector quantity).

E = −\[\frac {dV}{dr}\]

• The negative sign indicates that the electric field points in the direction of decreasing potential — it does not mean the field itself is negative.
• In three dimensions, this generalises using the gradient operator: \[\vec{E}=-\nabla V=-\left(\hat{i}\frac{\partial V}{\partial x}+\hat{j}\frac{\partial V}{\partial y}+\hat{k}\frac{\partial V}{\partial z}\right)\]