Answer:
[tex]W_{AB} = EqL[/tex]
Explanation:
The work done by the electrostatic force is
[tex]W_{AB} = \int\limits^A_B {\vec{F}(x)} \, d\vec{x}[/tex]
where F can be calculated by Coulomb's Law:
[tex]\vec{F} = \frac{1}{4\pi \epsilon_0}\frac{q_0q_1}{x^2}[/tex]
We can express this equation by the variables given in the question.
Electric field is denoted as E.
[tex]\vec{F} = \vec{E}q = Eq~(+\^i)[/tex]
The distance, x, is given as L. If B is greater than A, the work done is positive. Else, work is negative.
[tex]W_{AB} = \int\limits^A_B {\vec{E}q} \, d\vec{x} = Eq(B-A) = EqL[/tex]
