What is Potential Difference?

First off, let me just say that it is a nightmare trying to learn about electricity on the Internet. Over 90% of what you see is simply not true and you should only believe credible sources (i.e. someone who gives his/her name and profession) not some anonymous person on a forum. So with that said I have not given my name or profession, so if you follow my own rule you should not read this, but please do because I can say that I have had enough of a post secondary education on electrodynamics to explain potential difference, and I will try my best to give analogies along the way to help in understanding.
First, We need to understand what electric potential is to get potential "difference". Electric potential
represents the sum of an electric field's strength at every point over some distance. Usually we like to integrate(another word for "sum" or "add") from a known point to another point of zero electric field strength, i.e. usually infinity. Once we have integrated the electric field strength over this distance we call its value "potential." Which is in simple terms: V=E*d assuming electric field is uniform. Now that we know the potential at point A in reference to zero electric field strength and we also determined the potential at point B in reference to zero electric field strength, we can subtract the two from each other and get the potential "difference."

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Electric Field From Point Charge

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Electric Field from Two Ends of Battery, Superimposed

Above images display electric field lines. The potential difference between a battery's electrodes is found by integrating the nonuniform electric field from one end to the other.
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Integral of Electric field as a function of position from A to B on e-line, times the infinitesimal e-line component.
(Basically: the sum of the electric field from A to B.)

Important to know: The word "potential" in potential difference is considered to be a misnomer by many physicists, engineers, and scientists because it sounds like potential energy. Which it is not.


Now that I mentioned energy, I might as well talk about it:


Analogy: Take a ball suspended 10 meters above ground. This ball has a mass of 1 kilogram and a charge of 1 coulomb. Earth produces a gravitational field such that the force applied to an object is proportional to the object's mass; thus exerting a constant and same acceleration on all objects on earth. This acceleration is 9.8 m/s/s. You can probably guess what this ball's potential energy is. It's mass*accelofgravity*height, which equals 98 joules (unit for energy). As you can see it's potential energy did not depend on the charge of the ball.


Now let's take this same ball and suspend it again at 10 meters. This time we are suspending it above a giant charge of no mass. This giant, massless planet produces and electric field of 9.8 V/m at the surface. If the ball has the same charge and mass as before what do you think it's potential energy is? Well, it's electricfield*charge*height which is 98 joules. As you can see it's potential did not depend on the mass of the ball but rather on the charge of the ball.


Hope this helped.


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