Derive an expression between Electric field and electrostatic potential due to a point charge. Also,why there is a negative sign in the expression.

Objects may possess a property known as an electric charge. An electric field exerts a force on charged objects, accelerating them in the direction of the force, in either the same or the opposite direction of the electric field. If the charged object has a positive charge, the force and acceleration will be in the direction of the field.

 

he potential of an electric field is called  the electric potential. The electric potential (or potential) at a point in an electric field is defined as the work done in moving a unit positive charge from infinity to that point.

 

The electric potential at a point r in a static electric field E is given by the line integral

where C is an arbitrary path connecting the point with zero potential to r

BEcause the work is done against the direction of electric field, the sign is negative.