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## Electrical engineering

### Unit 5: Lesson 1

Electric force and electric field

# Coulomb's law

Sal explains the fundamental force that causes charged particles to attract or repel each other.

## Want to join the conversation?

• How do we know that there are only two types of charges and not three? •   Great question! A complete answer to this requires very advanced mathematics, unfortunately, but I will try to give a taste of the idea. First, you have to know this secret: almost everything you learn in the first three years of physics is not really true. Newton's law of gravity, Coulomb's law of electrostatics, and Maxwell's laws of electromagnetism are all just approximately true, for systems which are on the human scale of time, space, energy, and speed. For hundreds of years, people thought Newton and Coulomb had found the EXACT FINAL PERFECT TRUE laws of physics, and only in the 20th century, when relativity and quantum mechanics were discovered, did physicists learn that the truth is totally, radically different from these laws for very tiny objects and high speeds.

So, for every force, it turns out that there is not really a "field" in the way we learn in intro physics, but instead the "force" is caused by the exchange of some particle. For the electric force, the force-carrier is the photon, which is sort of like a "chunk" of oscillating electromagnetic field which flies around at the speed of light. Every force also has a mathematical symmetry associated with it, and for the electric force that symmetry is the symmetry of the circle (this is called the "U(1) symmetry group"). If you think about a circle with some points on it labeled, the only thing you can do to it that will leave it exactly the same is rotate it an integer number of times. Putting this together with a lot of very advanced math, the result is that electric charge has to come in integer amounts. So it's not exactly that there are "two types" of electric charge, but more like "electric charge must come in chunks of ..., -3, -2, -1, 0, 1, 2, 3, ..." (i.e. integer number of chunks. the size of that chunk can only be discovered by experiment).

Now, you might then ask, "But how do we know that the symmetry is U(1)?" The answer to that would be that we can only guess what the symmetry is and then do experiments to find out. It turns out that if the symmetry group is not U(1), then the force-carriers must themselves carry some kind of charge, and that would mean that photons would significantly affect other photons! But if you do the experiment of crossing two laser beams, you can see that light (photon beams) has no direct effect on other light. Charged particles (electrons and protons) affect (produce, absorb, bend) light, and light (or radio waves or x-rays, they are all photons) affects charged particles, but light passes straight through other light. This shows that the symmetry of electromagnetism is U(1), and thus that electric charge comes in integer chunks.

Other forces have other symmetries, though! For example, the symmetry of the strong force (which holds the quarks together inside protons and neutrons, and holds the protons and neutrons together inside atomic nuclei) is a much more exotic symmetry called "SU(3)". This means that the force-carrying particle of the strong force (called "gluons") DOES come in more than two types. The "charge" for the strong force is called "color charge", and comes in THREE types, which physicists call red, green, and blue. It also means that the particles which are exchanged to produce the strong force, gluons, carry "color charge" themselves, unlike photons which have no electric charge. So a beam of gluons would not just pass through another beam of gluons like one laser beam does pass through another.
• • It's because we already know that the charges will attract (in this case) each other as one is positive and the other is negative. In any case, we can visually determine this property of the question based on the type of the charge. So if we happen to calculate the force between like charges, we know that there will be repulsion, whether large or small in magnitude. On the other hand, if we calculate the force between unlike charges, we know that there will be attraction, whether the magnitude of that attraction is large or small. So we are actually calculating the magnitude and not the direction. We can visually determine the direction.
• the gravitational force does not depend up on medium,but why electrostatic force does? • at why does the denominator change from 0.5 to 0.25? • Why does Coulomb's law use the 'metres' unit instead of a far smaller unit like micrometres or something? It seems really inefficient to describe such small variables as atoms in terms of such large distances. •  The meter is the standard unit of length for the SI system. It is not all that common to use irregular units like cm or mm because the units are easily confused when performing a calculation. It is standard practice to use all base units whenever possible and take care of the large/small number problem with scientific notation. Also, Coulomb's law is used to determine the force between point charges, not necessarily atoms. It is frequently used on the macroscopic scale in which meters are fully sensible.
• How can we say that the force varies as 1/r^2 and not as 1/r^2.0001? • • It depends on the scale of the objects and the amount of charge. In the case of two small, charged particles, the electrostatic force will be greater than the gravitational force because its mass is so small. However, two large planets (with large mass and no net charge) will have a stronger gravitational force. You can prove this by plugging in the values to both Coulomb's law (F = k*(|q1*q2|)/r^2, and Newton's Law of gravitation. (F = G*(M1*M2)/R^2).
• I have heard that charged and neutral objects attract each other. But in the formula
F=k*q1*q2/d^2, if we substitute q2=0, the result that we get is zero. How is this possible?   