Electrical Engineering ⇒ Topic : Potential Gradient

Potential Gradient

The change of potential per unit distance is called potential gradient i.e.

where V₂ - V₁ is the change in potential (or p.d.) between two points S metres apart. Obviously, the unit of potential gradient will be volts/m.

Consider a charge +Q and let there be two points A and B situated S metres apart in its electric field as shown in Fig.(A).Clearly, potential at point A is more than the potential at point B. If distance Sis small, then the electric intensity will be approximately the same in this small distance. Let it be E newtons/coulomb. It means that a force of E newtons will act on a unit positive charge (i.e. + 1C) placed anywhere between A and B. If a unit positive charge is moved from B to A, then work done to do so is given by ;

                                         Figure (a)

Work done = E x S joules

But work done in bringing a unit positive charge from B to A is the potential difference (V_A - V_B)between A and B.

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Hence electric intensity at a point is numerically equal to the potential gradient at that point.

Since electric intensity is numerically equal to potential gradient at any point, both must be measured in the same units. Clearly, electric intensity can also be measured in V/m. For example, when we say that potential gradient at a point is 1000 V/m, it means that electric intensity at that point is also **1000 V/m or 1000 N/C.