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A Few Facts On Coulomb’s Law

A few words on the modern interpretation of Coulomb’s Law in terms of Fields Theory.

At the base of all the electromagnetism theory lays Coulomb’s Law, which describes why and how charges move in a medium, whether the medium is a conductor or the void.

Electrical and Electronics engineers are therefore supposed to be very familiar with this law. Let’s spend some time to provide a few important facts of the law. For that, we have to go back to the concept of ‘field’.

In modern physics, we usually tend to identify the effect of an entity over another entity with the name of field. Mathematically speaking, a field is a 3-dimensional matrix that assigns a specific value, usually a vector, to each point in the observed space.

Each time we put in that space an object capable of reacting with the field, we end up with a force applied to that object that is the product of the field in that point and the measurable value of that object.

So, in the case of charges, a single charge creates a field in the surrounding space. When we put in that space a second charge, the new charge will be subject to a force that is the product of the charge itself and the value of the field in that point in space.

Because charges can repel or attract, depending on their positive or negative sign, the field itself is directional, and therefore represented with vectors..

Here is a picture representing a field generated by a positive charge:

And here is a picture representing a field generated by a negative charge:

If the charge creating the field is Q, then the field can be represented by the following equation:

where E is the value of the field, actually the module of the field vector, and r is the distance from the charge of a point in space where the field is calculated. The constant ε₀ is called “dielectric constant” and, in this formula, it assumes that the charge is located in the void or in thin air. An adjustment to the constant needs to be made when the medium is different.

We call this field an Electrostatic field, hence the E, because the charge that generates it does not move, it is static.

The force on a charge q put in the field can be calculated as:

And, since E is actually a vector, F is therefore also a vector.

If we want to represent this in actual vector format, we can write it as:

where

is the position vector of the charge q with respect to the charge Q. This is what is called Coulomb’s Law.

You can see that if the charges are both positive or both negative, the vector F is oriented such that the charge q moves away from the charge Q and, vice versa, when the charges have opposite sign, F is oriented toward Q.

That is exactly what we expected: charges of the same sign repel each other and charges of opposite sign attract each other.

As a further example, here is the graphical representation of an electrostatic field generated by two charges of opposite sign:

… and finally an electrostatic field generated by two charges of the same sign:

Let’s Talk About Voltage

What is voltage? Where the name comes from? How it makes electric current flow?

transmission_lines_scaled

Voltage is a very common word in the context of electrical and electronics engineering. However, common as it is, it is a concept that is often not fully understood.

How many people know that voltage is a concept related with potential energy? The same kind of energy that is so often used in mechanical physics!

When we talked about electrical current in the previous post, we said that current moves from a higher electrical potential energy to a lower one. We also defined the current as the flow of positive charges moving from the positive electrical potential energy to the negative one.

charges_in_wire

In order for the charges to move, there has to be a force that puts them in motion in a specific direction. Such force will have to do some sort of work on the charges and the work done by the force can be translated in a change in energy of the charges.

We define Electromotive Force the ratio between the energy change of the charges and the amount of charges. This can be represented with the following formula:

emf

Note that, despite the name, the Electromotive Force is not a force in the mechanical sense. Instead it is a potential energy per unit of charge, which we also call electric potential, or just potential.

The unit for the emf is called Volt, and is the ratio between one unit of energy, or 1 Joule, and one unit of charge, or 1 Coulomb:

volt

And that’s where the name voltage comes from: it is a name derived from the measurement unit of the electric potential. Although the correct name is electric potential, to make things easier in the day to day talk, we just call it voltage.

So, again, what is voltage? The voltage is the difference of electrical potential energy that allows a unit of charge to move and produce a current.

Now, do you think it is correct to say that when there is voltage we have a current? Do the two things always go together? Well, the answer is no. You can actually have one without the other.

An example of voltage without a current is the battery. If you don’t connect the battery to a circuit, there is no current involved!

batteries

And what about the current? This example is definitively less intuitive. So, let’s just say for now that if we force a current in a ring of a special material called superconductor and then we remove the cause that generated the current, the current keeps flowing in the superconductor, even in the absence of a voltage. Maybe we can explore this concept a little more in a future post, if I see there is an interest for it. Translation: let me know what you think! Comments are always welcome!

superconductor_ring

Let’s now go back to the battery. The battery provides a voltage between its positive and negative poles. With that, if we connect the battery to an electric load, current starts to flow immediately and the higher the voltage the greater the amount of current (more on that in a future post).

current_with battery

Like the current, there are two forms of voltage:

The DC voltage
The AC voltage

The DC voltage is the one typically provided by batteries. It is a voltage of a fixed value and of fixed polarity. The plus and minus on the electrodes of the battery never change. One electrode will always be the positive one, and the other electrode will be the negative one.

When we connect a battery to an electric circuit, we have a flow of DC current.

The AC voltage is the one created for example in the power plants and provided at the wall outlets in your house.

power_plant_scaled

outlet_scaled

The voltage at the outlet is not constant as the one in the batteries. Instead, it changes continuously following the shape of a sine wave. Because of that, the polarity at each electrode of the outlet changes over time from positive to negative and vice versa, following the shape of the sine wave.

sine_wave

When we connect a device to the electric outlet, the current that will flow through that device will be an AC current as well.

The sinusoidal shape of the AC voltage depends on the way the electricity is generated. In the power plants there are devices called alternators, a much bigger version of those that you can find inside your car to recharge the battery, or on a bike, to provide electricity to turn on the lights at night.

Depending on the power plant, a different kind of energy is used to put in motion the alternator. It could be fossil fuel or nuclear energy that heat a reservoir of water and create the steam that makes the alternator rotate.

big_alternator_scaled

Or it could be the rotation of a propeller-like device that is put in motion by the wind.

propeller

Whatever the source is of the mechanical energy, the alternator converts that energy in electrical energy. But, since the rotation translates into a sine wave when described on a Cartesian reference system, the resulting electrical energy acquires that shape too.

DC and AC are both necessary to us to power devices that make our lives easier. Some devices need to be powered with DC, others need the AC.

DC voltage is necessary, for example, to power electronic devices: your smartphone or radio or computer, for example.

AC voltage is used to transmit the electrical energy from the places where it is created to the places where it is used. When AC reaches our home, it can be used as is to power electric motors like those in the refrigerator or the washing machine, or other household appliance. Or it can be converted to DC to power other devices, like your TV set.

Summarizing:

To generate a current, we need to provide some energy to the charges in the conductor.
The potential energy per unit of charge is called emf, or electromotive force. That measures the capability of the generator (a battery, for example) of generating a current.
Most used synonyms of the emf are: voltage, difference of potential, and potential. Somebody also uses the name “tension”.
The measurement unit of the potential is the Volt, which is the potential energy of 1 Joule per unit of charge, or 1 Coulomb.
The Volt is a differential measure, not an absolute one. You always measure Volts with respect to a point that we arbitrarily define as 0V, or ground.
Emf can be DC or AC and, correspondingly, it can generate a DC or an AC current when connected to an electrical circuit.
DC voltage is normally generated through chemical reactions in a battery, or can be obtained from the AC through a process called “rectification”.
AC voltage is normally generated with alternators like those used in power plants.

If you want to know more on this topic, I suggest you to watch the companion video of this article, which I posted on my YouTube channel:

https://www.youtube.com/watch?v=vPX-B4xAdtk

Thank you for reading this article and, as always,

Happy Experiments!

Electric Current The Easy Way

Electric Current The Easy Way: a very simple and qualitative approach to understanding what electric current is and how it flows.

Watching a number of YouTube videos, I realized there is some misconception regarding the electric current and how it flows. Some people don’t understand what the current is made of and whether it flows from positive to negative or vice versa.

So here I am, trying to shedding some light to clear the obscurity on this subject.

This post approaches the subject in a very basic qualitative way. No formulas and no calculations are involved.

Here it is!

From the Webster Dictionary

Current:
A flowing or passing; onward motion. Hence: A body of
fluid moving continuously in a certain direction; a
stream; esp., the swiftest part of it; as, a current of
water or of air; that which resembles a stream in motion;
as, a current of electricity.

So, current is the flow of something, some kind of material thing like the molecules of water in a river.

fresh river_400

But, what is the material that makes the electric current?

Electric current is made of electric charges. These charges have the ability of moving in a medium like, for example, an electric wire. Like the water in a river, charges have to move from a higher level to a lower level of potential energy.

charges_in_wire

For a river, the higher level of potential energy is the higher ground, and so the water flows from a higher ground to a lower ground, from a mountain or a hill toward the valley below or the sea, or the ocean.

Similarly, for an electric current, charges have to move from a higher ground of electric potential energy to a lower ground.

The problem with the electric current is that different kind of charges can make it, depending on the medium, and depending on the kind of charges. So, the definition of higher ground may change.

This seems utterly complicated, and it is. Think if we had to consider the kind of medium and/or the kind of charge every time we need to describe what happens with a current.

So, since we don’t like complications, we make some simplification. We always define a higher ground as a positive electric potential energy level, and we always say that the current flows from the positive potential energy level to the negative.

positive_charges

Hum… Positive? Negative?

Well, yes, because charges can only be positive or negative. Think at the electrons and the protons in the atoms. Those are the basic charges and they are negative for the electrons and positive for the protons.

protons_and_electrons

Wait, what we just said? Electrons are charged negatively and protons positively? How do we know that?

We don’t!

Positive and negative are just made up names that we use because it is convenient to do so.

We could have as well said that electrons are positively charged and protons are negatively charged. But, historically, we have defined the polarity of the charges in a certain way and therefore we continue to do so, because we don’t like changes, and we like concepts to be simple.

So, here we are, saying that an electric current is made of charges. That the charges can be positive or negative. That positive charges like to go from their kind of higher ground, a positive electric potential level, to a lower ground, which is a lower positive electric potential level that we call negative, to distinguish from the other one. And, finally, we say that negative charges like to go from their kind of higher ground, the negative electric potential level, to their kind of lower ground, which now we understand we can call positive electric potential level.

Hum, it seems too much, isn’t it?

And yes, it is: too complicated to use it in every day conversations.

Simplification? Sure, let’s do that. Let’s say that whenever an electric current is involved, we will always say that it is made up of positive charges, and that positive charges always go from positive to negative electric potential level. How’s that? Simple enough?

Now doesn’t matter the medium being an electric wire, were the current is made up of electrons moving through it, or the acid solution in a car battery, where the electric current is made of ions, of both positive and negative kinds, creating two different currents flowing simultaneously in opposite directions.

solution

Lesson learned: we like to make things simple. We define the electric current as the flow of positive electric charges in a medium, whatever it is, going from the positive potential level to the negative.

circuit

And that’s it. That’s enough for us. With this definition we can address problems involving electric currents always the same way, without worrying what is really happening behind the scenes. This is a very important concept. All about electrical engineering is based on this definition of current. Well… at least part of it.

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