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Potential Difference

Potential difference (ΔV) between two points is the negative of the work done per unit charge to move a charge between those points: ΔV = -W/q.
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The statement of the theorem

Let ϕ(r⃗)\phi(\vec{r}) be the scalar electric potential function defined over a region Ω⊂R3\Omega \subset \mathbb{R}^3, such that the electric field E⃗\vec{E} is derived from it via the gradient relationship E⃗=−∇ϕ\vec{E} = -\nabla \phi. The potential difference ΔV\Delta V between two points AA and BB is rigorously defined as the difference in the potential function evaluated at these points: ΔV=ϕ(B)−ϕ(A)\Delta V = \phi(B) - \phi(A). Alternatively, and equivalently, ΔV\Delta V is defined by the negative line integral of the electric field along any continuous path CC connecting AA to BB: \n\nΔV=−∫ABE⃗⋅dl⃗\Delta V = -\int_{A}^{B} \vec{E} \cdot d\vec{l} \n\nDue to the conservative nature of the electric field, this integral is path-independent, meaning that for any two paths C1C_1 and C2C_2 from AA to BB, the following equality holds:\n\n∫C1E⃗⋅dl⃗=∫C2E⃗⋅dl⃗\int_{C_1} \vec{E} \cdot d\vec{l} = \int_{C_2} \vec{E} \cdot d\vec{l}
Source: Wikipedia