Electric Potential Difference and Work

Between points `A` and `B`: ΔV = V_B − V_A Potential-energy change: ΔU = qΔV Therefore: ΔV = ΔUq For work done by the electric field: W_field = −ΔU so: W_field = q(V_A−V_B) For an external agent moving the charge slowly with no change in kinetic energy: W_external = ΔU = q(V_B−V_A) A potential difference of `1 V` means that the electric potential energy changes by `1 J` for every `1 C` of charge.

For a uniform electric field and displacement `d` parallel to the field: **ΔV = −Ed** The negative sign shows that electric potential decreases in the direction of the electric field.

**ΔV=ΔUq ΔU=qΔV W_field=−qΔV Uniform field: ΔV=−Ed** when displacement is along the field.