The relationship between electric field intensity (E) and potential gradient is given by:

E=−dVdxE = -\frac{dV}{dx}

Explanation:

1. Electric Field (E): It represents the force experienced by a unit positive charge in an electric field. Its unit is N/C or V/m.
2. Potential Gradient (dVdx\frac{dV}{dx}): It refers to the rate of change of electric potential (V) with respect to distance (x). A higher gradient means a stronger field.
3. Negative Sign (-): It indicates that the electric field points in the direction of decreasing potential. This means that a positive charge will naturally move from a higher potential to a lower potential.

Key Points:

• If the potential decreases rapidly, the electric field is stronger.
• If the potential varies slowly, the electric field is weaker.
• In a uniform field, E=−ΔVΔxE = – \frac{\Delta V}{\Delta x}.

This equation is fundamental in electrostatics and helps in understanding the behavior of charges in an electric field.