# Work needed to assemble charges vs. potential energy

I'm reading through an ENM text called Introduction to Electrodynamics by Griffiths, and in the section on work and energy, after giving the expression for work, he says:

"That's how much work it takes to assemble a configuration of point charges; it's also the amount of work you'd get back if you dismantled the system. In the meantime, it represents energy stored in the configuration ("potential" energy, if you insist, though for obvious reasons I prefer to avoid that word in this context.)

Those reasons aren't so obvious to me, lol. Why does Griffiths want to avoid the term "potential energy"? Seems to me like it makes sense, assembling point charges is analogous to holding a rock a few feet off the ground - there's energy stored in both, when released the rock falls down a gravitational gradient and when "released", a charge would "fall down" an electric gradient. What nuances am I missing here?

• $\uparrow$ Which page? Jan 29 '17 at 12:20
• Sorry for not including it initially - bottom of page 93 in the fourth edition. Jan 29 '17 at 12:34
• Have a look at **2.3.2 Comments on Potential (i ) The name ** a few pages back where all is explained. Jan 29 '17 at 17:24

Why does Griffiths want to avoid the term "potential energy"?

Because electric potential and potential energy are two different things.They are related ofcourse but they are different.(check page number 80).

You may be thinking that

"Electric potential energy of a charged object at a point is the amount of work done to bring that object from infinity to that point
and electric potential at a point is just amount of work done needed to bring an object with unit charge to that point from infinity .So potential energy and potential are nearly same thing".

This is correct but not always .It is only correct when the reference point is at infinity.

$$\text{Electric potential} =\dfrac{\text{electric potential energy}}{\text{charge}}$$

This equation is only true when the reference point is at infinity . But electric potential and potential energy in general are different things really.

So to avoid confusion call potential energy ,the electrostatic energy .

One way to create a point like particle with charge is to consider an infinite charged sphere and contracting it to a point. The initial configuration has vanishing potential energy since the partial charges are separated by infinite distances

$$1/r\xrightarrow{r\to \infty}0$$

If we now contract this to a point-like particle we get a infinite expression $$1/r\xrightarrow{r\to 0}\infty$$ This simple argument shows that taking into account the energy needed to create a given charge distribution would destroy any attempt to calculate reasonable quantities, since one would get some $\infty\pm \infty$-like expressions. To avoid this one only takes into account the potential energy due to the forces between the particles, neglecting the energy needed to create the involved point-like particles.

You see, due to our need to remove the point-particle-creation-energy it is not available anymore and therefore one should avoid to speak of it as potential energy, which in contrast is available energy, which triggers processes in the system.

The potential energy is the work done to move one charge from infinity to a location specified by $\vec r_p$ in an external field. The energy mentioned in this problem applies to the work done to move a collection of charges.

It is a sum of potential energies, representing work done in moving the constituent charges one after the other from infinity to their final positions, i.e. moving charge 2 in the field of charge 1, moving charge 3 in the field of charges 1 and 2, and so forth until the final charge distribution is in place.

If you consider system with two point charges, it's potential energy is total amount of electrostatic energy that can be derived by completely dismantling that system. So it has two component -

1. Energy required to bring charge from infinity to build point charges i.e. self potential energy of point charges. This component is infinite as point charges have zero radius and infinite amount of energy will be required to confine charge to zero volume. (But in reality, there is nothing like point charge - even electrons have some finite radius and hence only finite amount of self potential energy.)
2. Second component is energy required to bring two charges particles from infinity to their current position. And that is what book says as "Energy stored in configuration."