derive relationship between electric field intensity and potential gradient at a point in electric field

The electric field intensity at a point can be defined as the negative of the potential gradient at that point. i.e.
Electric field intensity = - Potential gradient  E = – dV/dx.
;the negative sign - implies that measuring from the positive plate the potential drops with increasing distance.
In the uniform field the electric field intensity is the same anywhere in the field and therefore you should see that the potential decreases steadily with distance from one plate to the other.
[dV = -Edx]

  • 1

Analytical treatment

Here's a an interpretation of what gradient means.

Gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase or decrease of the scalar field, and whose magnitude is that rate of increase or decrease.

Electric field in space will point in the direction where the rate of decrease of potential is maximum.

In the diagram the maximum decrease is along V- VA 

  • 4
What are you looking for?