Show that potential difference can be described as energy transferred per unit charge between the two points.

The potential difference, ΔV, between two points in the electric field can be described as the potential energy transferred per unit charge, ΔU/q₀ , between the two points

ΔV = ΔU/q₀

Explanation:

The force, F, acting on a test charge, q₀, placed in an electric field E is given as follows;

F = q₀·E

The work the electric field does on the charge, W =dU =  F·ds = q₀·E''·dS

The electric potential difference, ΔV, between two points in the electric which is the change in the energy of the system when a test charge is moved between points in the field is goven as follows;

Therefore, given that, we have;

Therefore, the potential energy transferred per unit charge, ΔU/q₀ can be described as the potential difference between two points in the electric field, and vice versa.