electrostatics - Electric potential vs potential difference

What is the difference between electric potential and potential difference? In our course book, they are given as separate topics but their definition is given the same.

Answer

What is the difference between "electric potential" and "potential difference"?

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What is the difference between age and age difference?

If $\text{age}(\text{person})$ is the function so that $\text{age}(\text{you})$ is your age, $\text{age}(\text{mom})$ is your moms age and $\text{age}(\text{dad})$ is your dads age, then $\Delta\text{age}:=\text{age}(\text{dad})-\text{age}(\text{mom})$ is the age difference of your parents.

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The elecrical potential $\Phi$ refers to a quantity with some numberic value. It is usually dependent on space and time $\Phi(\vec x,t)$, so it's a field where for every place and moment you get some number.

By potential difference $\Delta\Phi$ one denotes the difference between two such values taken at different positions. For example,

$$\Delta\Phi:=\Phi(\vec x_2,t_0)-\Phi(\vec x_1,t_0)$$ is the potential difference of the field $\Phi(\vec x,t)$ for the two points $\vec x_2$ and $\vec x_1$ at the particular moment $t_0$.

So for example, if you have a one-dimensional capacitor with electical potential $\Phi(l)$, with one plate at the position $l=0$ and the other at position $l=L$, then the potential difference $\Delta\Phi$ for these two points is the number you compute via $\Phi(L)-\Phi(0)$.

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I think your question might arise because only the potential difference is the physical quantity which determines the electical field and therefore the acceleration of charges. While as age difference between persons as well as age of one person are both interesting quantities with practical value (Did I miss my mom's bithday? Am I allowed to drive? How much years will I get for homicide?), the value of the electical potential as such will eventually only be used to compute potential differences.