Page 13 - Electrostatics-11

© GC Shiba
Electric potential gradient:

Electric potential gradient in electric fields is defined as the rate of change of
-1
electric potential with distance. Its SI unit is vm .

let ∆ be the change in electric potential in distance ∆ then

Electric potential gradient = ∆
∆

∆
= lim ( )
∆ →0 ∆

=

Relation between Electric potential gradient and Electric intensity:

A B
+Q
r
r + Δr

r
Consider two points A and B in the electric field of +Q charge at distances r
and r + Δr respectively. Type equation here.

Let electric potential at point A is =V

& electric potential at point B is = + Δ

P.d. between A and B, = − = − ( + Δ )

Work done to move +1 charge from A to B = −Δ

Force on +1 charge × Δr = −Δ

or, E × Δr = −Δ

or, = − Δ
Δ

or, = −

Thus, Electric intensity is equal to negative of electric potential gradient. Direction

of E is along which electric potential gradient decreases.

12 Electrostatics