Derive an expression to find the work done by the electric force to move free charges in specified directions.

Explanation

1. When the ends of a conducting wire are connected to the terminals of a battery. An electric field is set up throught the conductor. This field exerts a force `(F_(e))` on the charge.
2. This force does some work to move the through a distance `tau` from A to B as shown in the figure.

3. We know that, the work is the product of force and distance along the direction of force.
Work done by the electric force on unit charge is `=(W)/(q)=(F_(e)l)/(q).`
This work done by the electric force on unit positive charge to it through a distance `'tau` from A to B is know as potential difference, denoted by V.
`thereforeV=(W)/(q)=(F_(e)l)/(q).`