Electric Potential Energy in a Uniform Electric Field

Consider a positive test charge at a point P in a uniform electric field produced by oppositely charged parallel plates. The electric field exerts a Coulomb force on the test charge, which is along the electric field direction.

If the test charge is moved from position P to Q, then the work done by the electric field is the integral of the product of the force and the displacement.

Here the force is one-dimensional, and the displacement is in the same direction as the electric field, resulting in positive work.

The electrostatic force is conservative. Thus, the work can be expressed as the difference between the electric potential energies at points Q and P.

Here, the electric potential at P is higher than at Q, and the electrical potential energy decreases when the test charge moves from P to Q.

The work done will be negative for a negative test charge, and the electric potential will increase if the test charge moves in the same direction as that of the electric field.