9 julio, 2024

Point charge: properties and Coulomb’s Law

A point load, in the context of electromagnetism, is that electric charge of such small dimensions that it can be considered a point. For example, the elementary particles that carry electrical charge, the proton and the electron, are so small that their dimensions can be omitted in many applications. Considering that a charge is punctual greatly facilitates the work of calculating its interactions and understanding the electrical properties of matter.

Elementary particles are not the only ones that can be point charges. So can ionized molecules, the charged spheres used by Charles A. Coulomb (1736-1806) in his experiments and even the Earth itself. They can all be considered point charges, as long as we see them at distances much greater than the size of the object.

Since all bodies are made of elementary particles, electric charge is an inherent property of matter, just like mass. You cannot have an electron without mass, and neither without charge.

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Properties

As far as we know today, there are two types of electric charge: positive and negative. Electrons have a negative charge, while protons have a positive one.

Charges of the same sign repel each other, while charges of the opposite sign attract. This is valid for any type of electric charge, whether punctual or distributed over an object of measurable dimensions.

Furthermore, careful experiments proved that the charge on the proton and the charge on the electron have exactly the same magnitude.

Another very important point to consider is that the electric charge is quantized. To date, no isolated electrical charges of magnitude less than the charge of the electron have been found. They are all multiples of this.

Finally, electric charge is conserved. In other words, electric charge is neither created nor destroyed, but it can be transferred from one object to another. In this way, if the system is isolated, the total charge remains constant.

Units of electric charge

The unit for electric charge in the International System of Units (SI) is the Coulomb, abbreviated with a capital C, in honor of Charles A. Coulomb (1736-1806), who discovered the law that bears his name and describes the interaction between two point charges. We will talk about her later.

The electric charge of the electron, which is the smallest possible charge that can be isolated in nature, has a magnitude of:

e– = 1.6 x 10 -16 C

The Coulomb is a fairly large unit, so submultiples are often used:

-1 milliC = 1 mC= 1 x 10-3 C

-1 micro C = 1 μC = 1 x 10-6 C

-1 nanoC = 1 nC = 1 x 10-9 C

And as we mentioned before, the sign of and- it is negative. The charge on the proton has exactly the same magnitude, but with a positive sign.

The signs are a matter of convention, that is, there are two types of electricity and it is necessary to distinguish them, therefore one is assigned a sign (-) and the other a sign (+). Benjamin Franklin made this designation, and also stated the principle of conservation of charge.

By Franklin’s time, the internal structure of the atom was still unknown, but Franklin had observed that a glass rod rubbed with silk became electrically charged, calling this kind of electricity positive.

Any object that was attracted by said electricity had a negative sign. After the electron was discovered, it was observed that the charged glass rod attracted them, and that is how the charge of the electron became negative.

Coulomb’s law for point charges

At the end of the 18th century, Coulomb, an engineer in the French army, spent much time studying the properties of materials, the forces acting on the beams, and the force of friction.

But he is best remembered for the law that bears his name and which describes the interaction between two point electric charges.

Let there be two electric charges q1 and q2. Coulomb determined that the force between them, whether attractive or repulsive, was directly proportional to the product of both charges, and inversely proportional to the square of the distance between them.

Mathematically:

F∝ q1 . q2 / r2

In this equation, F represents the magnitude of the force and r is the distance separating the charges. Equality requires a constant of proportionality, which is called the electrostatic constant and is denoted as what.

Thus:

F=k. q1 . q2 /r2

Furthermore Coulomb found that the force was directed along the line joining the charges. Then yes r is the unit vector along said line, Coulomb’s law as a vector is:

This form of Coulomb’s law applies only to point charges.

Application of Coulomb’s law

Coulomb used a device called torsion balance for your experiments. Through it it was possible to establish the value of the electrostatic constant in:

ke = 8.99 x 109 N m2/C2 ≈ 9.0 x 109 N m2/C2

Next we will see an application. We have three point charges qA, qB and qC that are in the positions indicated in figure 2. Let us calculate the net force on qB.

The charge qA attracts the charge qB, since they are of opposite signs. The same can be said about qC. The isolated body diagram is in figure 2 to the right, in which it is observed that both forces are directed along the vertical axis or y-axis, and have opposite directions.

The net force on charge qB is:

FR. = FAB+ FBC (Principle of superposition)

It only remains to substitute the numerical values, taking care to write all the units in the International System (SI).

FAB = 9.0 x 109 x 1 x 10-9 x 2 x 10-9 / (2 x 10-2) 2 N (+and) = 0.000045 (+and) No.

FCB = 9.0 x 109 x 2 x 10-9 x 2 x 10-9 / (1 x 10-2) 2 N (-and) = 0.00036 (-and) N

FR = FAB+ FCB = 0.000045 (+and) + 0.00036 (-and) N= 0.000315 (-and) No.

gravity and electricity

These two forces have identical mathematical form. Of course they differ in the value of the constant of proportionality and in that gravity works with masses, while electricity does with charges.

But the important thing is that both depend on the inverse square of the distance.

There is a unique type of mass and it is considered positive, so the gravitational force is always attractive, while charges can be positive or negative. For this reason, electrical forces can be attractive or repulsive, depending on the case.

And we have this detail that derives from the above: all objects in free fall have the same acceleration, as long as they are close to the Earth’s surface.

But if we release a proton and an electron near a charged plane, for example, the electron will have a much greater acceleration than the proton. In addition, the accelerations will have opposite directions.

Finally, the electric charge is quantized, as stated. That means that we can find charges 2.3 or 4 times that of the electron -or that of the proton-, but never 1.5 times this charge. The masses, on the other hand, are not multiples of some unique mass.

In the world of subatomic particles, the electric force exceeds the gravitational force in magnitude. However, at macroscopic scales, the force of gravity is the one that predominates. Where? At the level of the planets, the solar system, the galaxy and more.

References

Figueroa, D. (2005). Series: Physics for Science and Engineering. Volume 5. Electrostatics. Edited by Douglas Figueroa (USB).
Giancoli, D. 2006. Physics: Principles with Applications. 6th. Ed Prentice Hall.
Kirkpatrick, L. 2007. Physics: A look at the world. 6ta abridged edition. Cengage Learning.
Knight, R. 2017. Physics for Scientists and Engineering: a Strategy Approach. pearson.
Sears, Zemansky. 2016. University Physics with Modern Physics. 14th. Ed. V 2.

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