Definition of electric potential difference

We define the potential difference between two points A and B as the work done by an external agent in moving a test charge q_o from A to B i.e.

V_B-V_A = W_AB / q_o          

The unit of the potential difference is (Joule/Coulomb) which is known as Volt (V)

Notice

Since the work may be (a) positive i.e V_B > V_A

  (b) negative i.e V_B < V_A

    (c) zero i.e V_B = V_A

You should remember that the work equals

• If 0 < θ < 90 ⇒ cos θ is +ve and therefore the W is +ve

• If 90 < θ < 180 ⇒ cos θ is -ve and therefore W is –ve

• If θ = 90 between Fex and l ⇒ therefore W is zero

The potential difference is independent on the path between A and B. Since the work (W_AB) done to move a test charge q_o from A to B is independent on the path, otherwise the work is not a scalar quantity.