RELATION BETWEEN POTENTIAL GRADIENT AND ELECTRIC INTENSITY

Potential gradient g is defined as:

g=dVdx

                                ..........................................(1)

Electric field E is defined as:

E=−dVdx

                                .........................................(2)    

From equation (1) and (2)

E=−g

This shows that the potential gradient g at a point in the electric field is negative in magnitude of E at that point.

From the point of view of magnitude, both E and g are equal and this can be proved as under:

Since                                    

V=Wg

∴  1 volt=1 joule1 coulomb


But      1 Joule=1 newton×1 meter


∴  1 volt=1 newton×1 meter1 coulomb


or          1 volt1 meter=1 newton1 coulomb


∴  1 volt / meter=1 newton / coulomb


thus     unit of potential gradient=unit of electric intensity