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I'm studying electric potential energy and its defined as the energy needed to move a charge inside an electric field from a point $a$ to $b$. Then, it defines electric potential energy per charge, that is, given a charge, I can know the potential energy at any point of the system.

Now, I was watching a video about a person rubbing its feet on a carpet and getting electrocuted after touching the door's metal. The video says that this happens because the person had a higher electric potential compared to the door.

What is the electric potential in this case? More charge means more electric potential? I can't apply my definition of electric potential for a charged person, because the book defined electric potential energy for a particle far away from the charge source, but the person IS the charge source, how can It have potential at all?

I can, however, imagine lines of same electric potential around the person, but I don't understand how it can have an electric potential at all.

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In circuits it's obvious what a potential difference means, but I agree that it's harder to see what potential means for an isolated obect.

To address this we have a standard that the potential of a unit charge is zero at infinity. That is, if you take the unit charge an infinite distance away from the object you're considering, then the potential on the unit charge is defined as zero.

Let's take your example. Take an electron from the person, move it a long distance away and measure the work needed to do this. If the work needed is $W$ then we define the electrical potential of the person $V_\text{person}$ using:

$$ V_\text{person} = \frac{W}{e} $$

Now we can do the same with the door to get the electrical potential of the door $V_\text{door}$. If we discover that $V_\text{door}$ is more positive than $V_\text{person}$ that means it is energetically favourable to move electrons from the person to the door, and that's why the current flows.

Obviously the electrons don't actually move away from the person to infinity then back from infinity to the door. The moving to infinity is a thought experiment to illustrate how a difference between the potentials of the person and the door can be defined.

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only a charged body has electric potential around it. Since the person was positively charged by rubbing on carpet, he has a pistive potential around him. when person rubbed his foot on carpet he lost some of its electrons to carpet giving him positive charge. The definition given in book meant to present a view of how to calculate potential around a charged body and not that it has potential around it. From the definition given that to take charge from infinity to that point will give you magnitude of potential at that point.

Here that person has a positive potential around it because of positive charge on it. You can measure positive potential around him by using this definition. This +ve potential around him was because of him only, so it can be said he has positive potential or more correctly +ve potential around him.

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