## Monday, February 24, 2020

### Unizor - Physics4Teens - Electromagnetism - Electric Current

Notes to a video lecture on http://www.unizor.com

Electric Current

Conductors and Dielectrics

Electric current is a flow of electric charge. Since the actual carrier of electric charge is excess or deficiency of electrons, we need certain material where electrons can travel. So, vacuum cannot be a conductor of electricity because there is no electrons in it, but many metals, like copper, can. But we know that the electrons are orbiting the nuclei of the atoms. So, why do they travel?

The answer is: the force of an external electric field pushes or pulls electrons off their orbits and, as a result, they move inside the material where electric field is present towards or away from the source of the electric field, depending on whether the source is positively (deficiency of electrons) or negatively (excess of electrons) charged.

Consider a copper wire. It contains atoms of copper with 29 electrons in each atom, orbiting on different orbits around corresponding nuclei with 29 protons and from 34 to 36 neutrons in each.
Electrons stay on their orbit until some outside electric field comes into play. When it does, if its intensity is sufficient to push or pull light electrons off their orbits, while heavy nuclei stay in place, these electrons move in one or another direction as a result of different forces acting on them, the major of which is the intensity of the outside electric field. General direction of electrons is defined by the vector of intensity of the electric field. That makes copper a good conductor of electricity.

On the other hand, there are materials, like glass, where electrons are connected stronger to their nuclei, which makes more difficult to push them off their orbits. these materials do not conduct electricity, they are called insulators or dielectrics.

Ideal conductor, connected to an electrically charged object, makes an extension of this object. Since electrons are freely moving between the original object and an attached conductor, both constitute a new object with an electric charge evenly distributed between its parts.
Ideal dielectric, attached to an electrically charged object, does not share its electrons with this object, so the object remains the only one charged.

In practical cases there are no ideal conductors (except under certain conditions of superconductivity under temperatures close to absolute zero) and no ideal dielectrics (except absolute vacuum that has no electrons at all).

Metals are usually good conductors because their nuclei are relatively not easily moved from their places, while electrons are easily pushed off their orbits.
We use this property of conductors to direct the electrons to perform some work, like lighting the bulbs or moving electrical cars.

IMPORTANT NOTICE:
Conductivity is related to movement of electrons and is a measure of how easily electrons are pushed form their orbits by outside electric field.
This should not be mixed with permittivity defined for electric fields and is a measure of propagation of electric field inside some substance.

Electric Current

If the source of the field is a positive charge located near one end of a copper wire, electrons inside the wire would go towards that end. If the negative charge is the source of the field, electrons will move towards the opposite end.

If there is nothing on the opposite end of a copper wire, electrons, after being pushed towards one of the edges, will stop. If, however, there is an opposite charge on the other end of a wire, electrons will move from the negatively charged end to the positively charged one until both charges neutralize each other and whatever end was missing electrons (positively charged) will be compensated by electrons that are in excess on the negatively charged end.

Imagine now that we manage to keep one end of the wire constantly charged positively, while another end constantly charged negatively. Then electrons from the negatively charged end will flow to the positively charged end as long as we can keep these constant opposite charges on both ends. We will have a constant flow of electricity, which is called electric current (or simply current in the context of electricity).

This process of maintaining constant flow of electricity is analogous to maintaining constant flow of water down the water slide using a pump that constantly pumps the water from a pool to the top of a slide, from which it flows down because of the difference in heights and gravity.

While the presence of the electric field is felt almost instantaneously (actually, with a speed close to a speed of light), the electrons that carry electrical charge are not moving from a negatively charged end of a copper wire to the positively charged end with this speed.

A good analogy is the pipe filled with water and a pump connected to one of its ends. As soon as the pump starts working, the water it pumps starts its trip along the pipe and pushes the neighboring molecule of water. Those, in turn, push the next ones etc. So, the water will come from another end of a pipe almost instantaneously (actually, after a time interval needed for the sound waves in the water to cover the length of a pipe), but it's the "old" water already present in the pipe before the pump started working. "New" water that is physically pushed into a pipe by a pump will eventually reach the other end, but not that fast.

Finally, let's talk about measurement of the electric current.
The natural way of measurement of the flow of water in the pipe, as exemplified above, would be amount of water flowing out of a pipe per unit of time.
In our case of electric charge we can do the same - measure the flow by amount of electricity (in coulombs) traveling from one source of electric field to another (with opposite charge) per unit of time.

The unit of measurement of the electric current is ampere, where 1 ampere is the flow of electricity, when 1 coulomb of electricity is moving across the wire within 1 second.
1 A = 1 C / 1 sec.

Recall the definition of a unit volt as a difference in electric potential between points A and B such that moving one coulomb of electric charge between these points requires one joule of work. Therefore,
1 J = 1 V · 1 C
From the definition of ampere above
1 C = 1 A · 1 sec.
Therefore,
1 J = 1 V · 1 A · 1 sec
1 V · 1 A = 1 J / 1 sec
As we know,
1 J / 1 sec = 1 W (watt)
So, electric current of 1 ampere between points with difference of potential 1 volt performs work of 1 watt, that is 1 joule per second.

There is a direct analogy between electricity and mechanics with force analogous to voltage and speed analogous to amperage
Force · Distance = Work
Force · Distance / Time =
= Work / Time = Power

Force · (Distance / Time) =
= Force · Speed = Power

Voltage · Amperage = Power

Let's consider a slightly more complicated example of the electric current.
Assume that at one end of a copper wire we have a source of electric field with negative charge and at another end of this wire we have another source of electric field also with negative charge. Both ends will repel electrons inside a wire. However, if the charges are not equal, the larger one will push stronger, and electrons will move away from it towards the other end of a wire.

The situation with two unequal negative charges is analogous to a water pipe with two pumps of different power pumping water into it from both ends. The stronger pump will overcome the weaker and the water will move from a stronger pump to the weaker.

So, the most important factor in determining the direction of electrons in the wire is the intensity of electric field produced by electric charges. For multiple sources of electric field their vectors of intensity are added. From a general viewpoint, if there is a difference in intensity of electric fields, electrons will travel in the direction defined by a stronger force. In practical situation, when two sources of electricity are applied to two ends of a wire, one positive and one negative, one end attracts electrons and another pushes them away, the flow of electrons will be always from negative to positive charge.

Assume, the intensity of electric field at the end A of a wire is EA and intensity at the other end B is EB. If both charges at points A and B are positive or both negative, the vectors EA and EB inside a wire are oppositely directed. If the charges are of different sings (which is a typical situation in practical applications of electricity), these vectors are directed the same way.

The force acting on each coulomb of electricity inside a wire is a vector sum of both intensities:
E = EA + EB
The work needed to move one coulomb of electricity is, therefore,
W = E·L,
where L is the length of a wire.
This value W represents the difference of electric potentials of the electric field between points A and B, that is the voltage VAB between them.
The difference in intensity of an electric field corresponds to the non-zero voltage between these points.

If we can maintain the difference in electric field's potential between the two ends of a wire (non-zero voltage between them), the intensity of an electric field will push electrons from one end of a wire to another. This is how direct electric current is maintained.

As electrons move from one end to another, they leave "holes" - spots where they used to be, which are "moving" in the opposite direction. Since we conditionally associate "negative" charge with electrons and "positive" charge with the absence of electrons ("holes"), we can say that the direction of positive charges is opposite to that of negative.

For historical reasons, because electrons were not discovered yet, the direction of positive charges (that is, "holes" that are left, when electrons leave their places) was defined as a direction of the electric current.

The word direct means that the direction of the flow of electrons does not change with time and goes from the end with negative charge to the end with positive charge, which implies that the direction of the electric current (the direction of "holes" left by electrons) is opposite, from positive to negative end. For practical reasons we will not consider the case of the same sign of charges on both ends.

In most practical cases there is a device that separates the electrons from the neutral atoms within some object, thereby producing negative and positive charges on its terminals. If there is some conductor of electricity between these terminals, electrons will move from one terminal to another along this conductor, which constitutes a direct electric current in it.