Establish a relation between electric field (E) and potential difference (V) between two points in the field.
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Let us consider two equipotential surfaces A and B closely spaced.
Potential at A==V,Potential at B==V-dV
Where dV is the decrease in potential in the direction of electric field normal to A and B.
Suppose dr=perpendicular distance between the two surfaces.
Work done in taking a unit positive charge along dr from B to A
WBA=-E (dr)
Or WBA=Va-Vb = V-(V-dv)=dv
So -E (dr)= dv
Or E=-dv
dr
Potential at A==V,Potential at B==V-dV
Where dV is the decrease in potential in the direction of electric field normal to A and B.
Suppose dr=perpendicular distance between the two surfaces.
Work done in taking a unit positive charge along dr from B to A
WBA=-E (dr)
Or WBA=Va-Vb = V-(V-dv)=dv
So -E (dr)= dv
Or E=-dv
dr
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