# Infinite energy in a point charge

• mjordan2nd
In summary, Griffith explains that the point-like hypothesis is not true, as it breaks down when applied to smaller objects. He also mentions that general relativity would also have some limits to the point-like assumption.
mjordan2nd
What?

$$W = \frac{\epsilon_{0}}{2} \int E^2 d \tau = \frac{\epsilon_{0}}{2 \left( 4 \pi \epsilon_{0} \right)^{2}} \int \frac{q^{2}}{r^{4}} r^{2} sin \theta dr d \theta d \phi = \frac{q^{2}}{8 \pi \epsilon_{0}} \int_{0}^{\infty} \frac{1}{r^{2}} dr = \infty$$

Griffith explains this infinite energy coming from the charge being required to assemble itself. What does this mean? Surely tearing apart an electron would not solve all of humanities energy problems. Or is the problem that an actual unit of charge is discrete, whereas the equation treats it as a continuous charge distribution? I'm not sure I understand.

Last edited:
Point charges are "exact" as long as you don't get too close. Quantum theory takes over when r is small enough.

Don't worry, you are not misunderstanding or missing anything. The fact is, we have no idea what electrons (or any other fundamental particle) "are" or how they came to be--Higgs bosons aside, those types of questions belong in the realm of philosophers. Physicists can only measure the properties of a particle or object and its interactions, develop mathematical theories to fit the data, and accept that that is the way the universe chose them to be. Noone has ever made the claim that our system of language + mathematics provides a complete description of the universe--at least not without getting laughed at ;).

Randy

Well, if you drop the point-like hypothesis, you drop the problem.
It is clear that the point-like hypothesis cannot be true, if only for the problem you are just reporting.
There many known reasons to stop with the point-like hypothesis.
The 1/r² law has been discovered at least 200 year ago on macroscopic objects.
Applying it blindly down to the point-like size is meaningless.

Quantum mechanics is often cited as a cut-off for the point-like hypothesis. However, the point-like problem remains in quantum mechanics just as in classical physics. The Heisenberg uncertainties just tells us that the "point" cannot be located precisely, but he point is still within the assumptions. My understanding is that quantum electrodynamics tackles the problem more closely because of the coupling between fields and particles being treated in a fully quantum way.

Note also that general relativity would also come with some limit to the point-like assumption, since the electron could not be smaller than its Schwarzschild radius.

I think that our current understanding of the universe allows some people (but not myself) to talk about this topic without being laughed at.

Last edited:
My apologies for the late reply, but thank you for all of your responses. I take it that this is a strange quirk in electromagnetic theory. However, the mathematical argument seems unassailable, and consequently so do the results. So is the theory wrong, the math wrong, somewhere in between? I'm still a little lost as to why this happens.

Thanks.

The answer was given above. The point particle approximation must break down somewhere.

I see. Thank you.

mjordan2nd said:
My apologies for the late reply, but thank you for all of your responses. I take it that this is a strange quirk in electromagnetic theory. However, the mathematical argument seems unassailable, and consequently so do the results. So is the theory wrong, the math wrong, somewhere in between? I'm still a little lost as to why this happens.
You may find http://nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html" interesting on this point.

About 2/3 of the way down he talks about how he calculated the self-energy of the electron and determined that it was finite.

AM

Last edited by a moderator:
I haven't found Feynman's explanation very satisfying. If the two formulations are truly equivalent then there should be a way to achieve finite self energy with the field method. If not, then they are not truly equivalent, and so they are not describing the same physics. That is just my take.

## 1. What is the concept of "Infinite energy in a point charge"?

"Infinite energy in a point charge" refers to the theoretical concept that a point charge, which is a particle with a non-zero charge and no physical size, has an infinite amount of energy. This concept is based on the fact that the electric potential, or energy per unit charge, becomes infinite as the distance from the point charge approaches zero.

## 2. How does the concept of "Infinite energy in a point charge" relate to real-world scenarios?

In real-world scenarios, the concept of "Infinite energy in a point charge" is not applicable because point charges do not exist in nature. All particles have a finite size and cannot have an infinite amount of energy. However, this concept is useful in theoretical physics and can help explain certain phenomena, such as the behavior of charged particles in an electric field.

## 3. Can infinite energy be harnessed from a point charge?

No, infinite energy cannot be harnessed from a point charge. As mentioned earlier, point charges do not exist in nature and the concept of infinite energy is only applicable in theoretical scenarios. Additionally, the infinite energy of a point charge would violate the laws of thermodynamics, which state that energy cannot be created or destroyed.

## 4. What are the implications of the concept of "Infinite energy in a point charge" in the field of physics?

The concept of "Infinite energy in a point charge" has implications in the field of theoretical physics and can help explain certain phenomena, such as the behavior of charged particles in an electric field. It also highlights the limitations of our current understanding and theories of physics, as the concept contradicts the laws of thermodynamics and the principles of relativity.

## 5. How can the concept of "Infinite energy in a point charge" be reconciled with the laws of physics?

The concept of "Infinite energy in a point charge" is purely theoretical and cannot be reconciled with the laws of physics, specifically the laws of thermodynamics and the principles of relativity. It serves as a reminder that our current understanding and theories of physics may not be complete and there is still much to be explored and discovered in the field.

• Electromagnetism
Replies
4
Views
406
• Electromagnetism
Replies
10
Views
1K
• Electromagnetism
Replies
3
Views
300
• Electromagnetism
Replies
14
Views
2K
• Electromagnetism
Replies
1
Views
701
• Electromagnetism
Replies
19
Views
2K
• Electromagnetism
Replies
11
Views
810
• Electromagnetism
Replies
1
Views
943
• Electromagnetism
Replies
9
Views
930
• Electromagnetism
Replies
14
Views
1K