# Is there a universal repulsive force

## Coulomb's law: electrical force between charges

### Basics

There are two different types **electric charge**:

*positive*charge*negative*charge

Why, of all things *two* Types of cargo and not one or even three? Because the previous experiments (such as the deflection of charges in electric and magnetic fields) were able to find exactly TWO types of charge, which differ from one another in terms of their force effect. Positive charges repel each other with a certain force. Negative charges also repel each other. On the other hand, a positive and a negative charge attract each other.

Electric charge is abbreviated with a small \ (q \). And the physical unit of the electrical charge was defined as the unit "Coulomb" (\ (\ text C \)), which can also be written as an ampere second (\ (\ text {As} \)):

Remember that knowing the units can help you to derive other units or to check your transformations of formulas for correctness.

**Example of a charge**The electrical charge of a negatively charged electron is: \ (q = -1.602 \ cdot 10 ^ {- 19} \, \ text {C} \). Since it is the

*smallest*Charge that a free particle can have is also called this value of the charge

*Elemental charge*called \ (e \). The proton particle, on the other hand, has a positive elementary charge: \ (e = +1.602 \ cdot 10 ^ {- 19} \, \ text {C} \). The sign of the charge will determine whether the electrical force between two charges is repulsive or attractive.

### With what force do charges attract?

You now know that there are two different types of charge that exert a repelling or attractive electrical force \ (F _ {\ text e} \) on each other. You are likely to have some questions now: How can I calculate this force? What if the loads are different sizes? What if the distance between them is changed? All of these questions can be answered in one experiment. Coulomb's law is such a typical physical law, which was originally found out through experiment and not through a mathematical derivation.

Basically, the experiment on Coulomb's law goes like this: You charge two metallic balls electrically so that they carry an electrical charge that you specify, for example, by means of a voltage source. Then you measure the force between the balls, which are at a certain distance \ (r \) from each other. Then you vary both the distance (e.g. \ (0.1 \, \ text {m}, 0.2 \, \ text {m}, 0.3 \, \ text {m} \) ...) and the charges of one sphere \ ( q_1 \) and the second sphere \ (q_2 \) (e.g. \ (0.5 \, \ text {C}, 0.6 \, \ text {C}, 0.7 \, \ text {C} \) ...). A concrete experiment to determine Coulomb's law is, for example, the so-called *Coulomb rotary balance*.

All measured values you have collected are then further examined as usual in illustrative diagrams. In a \ (F _ {\ text e} \) - \ (r \) diagram (i.e. force as a function of the charge spacing) you will find that the electrical force between two charges \ (q_1 \) and \ (q_2 \) that the two balls carry, proportional to \ (\ frac {1} {r ^ 2} \) is:

That means: If you double the distance \ (r \), then the force \ (F _ {\ text e} \) decreases by FOUR times!

Then you look at how the force changes when you use different charge values. To do this, you vary the charge of a ball. You enter the measured values obtained in a \ (F _ {\ text e} \) - \ (q_1 \) diagram. As a result you get a linear relationship:

If you vary the charge \ (q_2 \) of the second sphere, you will of course get the same proportionality:

If you summarize the three experimental relationships, and then you already know the following proportionality:

Only the proportionality constant \ (K \) has to be determined in order to fully determine Coulomb's law:

By measuring the force between two (known) charges and their distance from one another, you can find out the constant \ (K \) you are looking for by transforming the equation. For example, charge the two balls so that they have \ (q_1 = q_2 = 10 ^ {- 4} \, \ text {C} \) and place them at a distance \ (r = 1 \, \ text {m} \) ) to each other. Then you will measure a force \ (F _ {\ text e} = 89.875 \, \ text {N} \) between the two charges. Move to the desired \ (K \) and insert the measured values provided here:

Of course, it doesn't matter which charges and which distance you choose, the result for the constant of proportionality will always be the same, because there is one *constant* is!

Later, in your physics adventures, it will turn out that it makes sense to define the Coulomb constant as follows:

That means with becomes the so-called **electric field constant** \ (\ varepsilon_0 \), which is in, by transforming from and then inserting to:

The unit of the electric field constant is usually in *Ammeter by volt-second* indicated, which can easily be done by unit conversion:

This important natural constant, i.e. the electric field constant \ (\ varepsilon_0 \) can be found almost everywhere where electricity and magnetism occur, because with the help of these natural constants, nature tells us how strong the electromagnetic interaction between electrical charges must be for the universe to be like this is how it is. *Why* It is precisely this value that is prescribed by nature, and not another, that can only be answered by a "higher power".

The journey ends here, because if you summarize everything you have learned so far, then you come to the following physical context, the one in honor of a French physicist *Charles Augustin de Coulomb*who experimented a lot with charges than **Coulomb's law** is called:

**Coulomb's law: electrical force between two charges**

### When is the electric force repulsive / attractive?

Depending on whether \ (q_1 \) or \ (q_2 \) in Coulomb's law is positive or negative, the electric force \ (F _ {\ text e} \) has a different sign and thus a repulsive or attractive effect on the two charges:

- \ (q_1 \) and \ (q_2 \) both positive. Then \ (F _ {\ text e} \) is also positive.
- \ (q_1 \) and \ (q_2 \) both negative. Then \ (F _ {\ text e} \) is positive, because "-" times "-" results in "+".
- \ (q_1 \) positive and \ (q_2 \) negative (or vice versa). Then \ (F _ {\ text e} \) is negative, because "+" times "-" results in "-".

### Force between electron and proton

**Example: force between electron and proton**Based on the simple atomic model of the hydrogen atom (hydrogen atom), orbits a

*negative*charged electron the atomic nucleus, which consists of a single

*positive*charged proton. Both the electron and the proton carry the elementary charge \ (e = \ pm 1.6 \ cdot 10 ^ {- 19} \, \ text {C} \). According to the model, the radius of the electron orbit is \ (r = 0.53 \ cdot 10 ^ {- 10} \, \ text {m} \). How big is the electrical force \ (F _ {\ text e} \) that the electron and proton exert on each other at this distance? Do you attract or repel?

Use Coulomb's law to find the electrical force between the two charges:

Since the force is negative, the electron and proton attract each other!

**Useful information!**Coulomb's law only applies in a vacuum or approximately in air. If you place the two charged balls in the water (of course no salty water, otherwise there will be a short circuit), you will find that the medium between the charges also plays a decisive role and we have not considered it! To take other media into account, the Coulomb law becomes: Here \ (\ varepsilon _ {\ text r} \) is the one introduced

**Dielectric constant**to account for the medium between charges. In the case of a vacuum, \ (\ varepsilon _ {\ text r} = 1 \). If the air in between is \ (\ varepsilon _ {\ text r} \ approx 1.0006 \). If there is lukewarm water in between \ (\ varepsilon _ {\ text r} \ approx 81.1 \).

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