# 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.

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The electric potential is the (electrostatic) potential energy per unit charge, $\Phi = E / Q$. – Luboš Motl Oct 16 '12 at 11:28
sorry for the inconvenience but now the question is corrected. I meant "potential difference" not "potential energy".. – Rafique Oct 16 '12 at 11:30
The difference means a subtraction. For example, the difference between 13 and 6 is 7. So if two potentials are 13 Volts and 6 Volts, then the potential difference is 7 Volts. There is no new physics term to be understood in "potential difference". One must just understand basic English and 1st grade basic school arithmetics. – Luboš Motl Oct 16 '12 at 13:12

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

What is the difference between age and age difference?

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

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 $\Phi(L)-\Phi(0)$.

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.

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Their definition may appear the same but quite different. I'm explaining it somewhat differently based on my sleepy experience in Electrostatics (which is pretty simple)...

Electric potential at a point in an Electric field (for instance, let's take it as uniform) is the amount of work done in moving a unit positive charge from infinity to that point against electric forces. (attraction or repulsion)

whereas Electric potential difference between two points in an Electric field is defined as the amount of work done in moving unit positive charge from one point to another point against the electric force.

In other words, Potential difference is simply the difference of scalar potentials between two points or anything you consider...

Now let's take an example. (I'm good at painting these stupid arts...)

Say, you're placing a charge (+q) at the point O. Also, There are two points A & B in the electric field $E$ (It acts outward since the line charge is positive). Now, you want to move a charge (say +q) from B to A. Then, you've to do some work against the force of repulsion. This work done is the potential difference between two points or Voltage (i.e.) $W_{B\to A}=dV$ which further equals $-E.dx$. Electric field is simply the force experienced by unit positive charge.

If you bring the same charge from $\infty$ instead of B, it's electric potential. Using the above figure & integrating for total work done (with limits $\infty$ to some scalar distance $r$), one could derive Electric potential at a point. It's given by $V=\frac{q}{4\pi\epsilon r}$. But, you could ask, "Why this work is not stored as some potential energy?"

Yes, It is. But, Potential energy requires the magnitude of another charge also... If $r$ is the distance of separation of two charges, P.E. is given by $E_p=\frac{qQ}{4\pi\epsilon r}$. In other words, $E_p=VQ$

That's why @Lubos pointed out that $V$ is the $E_p$ per unit charge... Hope you understand :-)

(Note: These could be used only in the presence of an Electric field..!)

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Potential is like the height position of water on the land. Under gravity, water will not flow between two points which are at the same height (zero potential difference).

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The amount of work done in bringing a unit positive charge fron infinity to a given point in electric field is called electric pontial at that point mathematically,

$$\phi=\frac{W}{Q}$$ Work W and charge Q. The work done in moving a unit positive charge from the point of lower potential to point of higher potential at the point is called electric potential differnce between two point

However both SI unit are volt. But they differ from each other.

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electric potential is the potential energy of a unit cahrge in any electri feild.where as elecric potential difference is the difference of electric potentials of two different points. it is equal to work done in carrying a unit positive charge from infinity to any point.

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## protected by Qmechanic♦Aug 17 '13 at 6:55

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