*Relation between electric field and potential*

Let
the small distance between A and B be dx. Work done in moving a unit positive
charge from A to B is dV=E.dx.

The work has to be done against the
force of repulsion in moving unit positive charge towards the charge +q. Hence,

dV= -E.dx

E= -dV/dx

The change of potential with distance
is known as potential dradient, hence the electric field is equal to the
negative gradient of potential.

The negative sign indicates that he
potential decreaces in the direction of electric field.The unit of electric
intensity an also be expressed as Vm

^{-1}
Why work done is Edx not Fdx

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