I'm just learning about electric potential in my second-semester physics class. My textbook is emphasizing the fact that electric potential is a property of the source charges and that I'll soon learn how electric potential and electric field are related.

In the meantime, I wonder if electric potential is a field in the same sense that electric field is. Can we draw electric potential field maps like we do for the electric field? I would suppose not, since electric potential is a scalar and not a vector. How should I picture electric potential then?

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    $\begingroup$ I think it's a scalar field. For every point in space, there is a value of $V$. $V(x, y, z)$. Whether or not the potential represents a real physical field ... I'll leave that to the philosophers. $\endgroup$ – garyp Dec 1 '15 at 19:54
  • $\begingroup$ There are a lot of semantic issues that could be addressed here. The potential is a field in the mathematical sense, but physicists typically attribute it less 'reality' as an independent object than the do the "electric field". $\endgroup$ – dmckee Dec 1 '15 at 22:16

I like to think about potentials as a hilly landscape. A ball rolling in this landscape will have an energy relative to how high the hill is wherever the ball is at. If it is up higher on the hill, the ball will have less kinetic energy, and lower in the valley, the ball will have more kinetic energy. The amount of kinetic energy the ball has is related to the height of the hill, and not the shape of the hill. The field can be thought of in terms of the shape of the hill. The shape of the hill can be described by its gradient, and this shape is going to tell you in what direction the ball will roll (or how it will change the trajectory of the ball), since the ball will want to roll downhill. Its convenient to think of it this way because the electric field is defined as the gradient of the potential.

So, the electric field is best visualized as a set of field lines, which tells you what direction the force applied is pointing at that particular point. The potential is best visualized as a contour map, telling you what areas are at a certain potential energy (landscapes can also be visualized by a contour map in the same way, showing the elevation or gravitational potential).


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