Why potential difference is not a vector

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I am a beginner in Electronics.
can anyone give me the most accurate explanation for why Potential
difference is a scalar, whereas electric field is ?

 

what is the direction of the potential difference? If there is a direction
you can have a vector; a la velocity vector.

 

It is like this: dV = -E(vector) dot dS(vector)

When you take the dot product of the electric field vector with the
direction vector you get a scalar quantity and that is the voltage.
Basic vector calculus,
the dot product of two vector quantities is a scalar quantity.

Rob

 

In short because the mathematics of the physics required it.

If the question is regarding scalar electric potential, V, vs. vector
magnetic potential, A, it can probably be attributed to the extra
degrees of freedom that come from magnetism being nothing more than a
relativistic correction of electrostatics. Because relativity
includes velocity, a 3-D vector quantity, magnetic potential probably
is vector simply because velocity is added into the mix.

MM