**Electrotechnics:** Basics

## Potential difference of charge. Work charge overcoming potential difference

### Movement of charge in an electric field

When the electric charge carriers is in the electrostatic field, it inevitably becomes effective Coulomb force. This leads to the fact that the charge carrier starts to move in the space, unless the Coulomb force is not compensated by the other, opposing forces. Consider the case where an electric field turned out to be a *probe charge* **q** completely free from the effects of other forces. As soon as the charge will be in the range of the electric field lines, then it will be a force in accordance with the Coulomb law.

As is known, the mechanical force is a vector quantity, and hence has the magnitude and direction. The charge carriers in the electric field starts to change its energy state. How does it manifest itself? Like charges repel and unlike attract. Our charge depends on the sign begins to approach him with the opposite sign of the charge, which is to form an electric field. This is most easily seen by looking at the lines of force of the field intensity. According to the rules, they have a referral from a of charge **+Q** to a charge **-Q**, in other words out of the *positive* charge (source), and enter the *negative* charges (the source).

The direction of force action on a probe charge **q** is very easy to determine if it is positive, then the force is directed along the field lines, and if negative, against force lines. The trajectory of the movement will depend on the initial velocity of the charge, its magnitude and direction. Acting force will accelerate the charge, that is, its velocity in magnitude and direction will change in the direction of action of the Coulomb force.

The figure shows an exemplary trajectory of the charge **+q**, has some initial velocity **V _{0}**. If the charge has the opposite sign, the trajectory of motion would be mirrored on the X, and the charge would be moved to the side of the plate (+). The Y-axis can be represented by a scale-building, which will also have the polarity.

Question. What is the scale and how to determine where more and where less potential? Given that, by definition, and according to the regulations field lines emerge from the charge (+) and go to infinity, where the potential is zero, the maximum positive potential will be the beginning of the field lines from the source, and the maximum negative potential where the lines enter the source field. Our charge **+q**, shown in the figure above will move from larger to smaller capacities, thus reducing the potential energy field, or rather, transforming it into kinetic energy. If in this case was a charge **-q**, then it would have changed the sign of the potentials, arithmetically, by multiplying by -1, it is all also be moved in the direction of decreasing the energy field.

### Potential difference - energetic characterization

Any charge during its motion in the electric field has a starting position field point in space, characterized by the potential **φ _{start}** and the end point, which also has the potential

**φ**. The difference between these two values is called the potential

_{final}**Δφ**- a potential difference, otherwise also known as the electric voltage.

One should distinguish between the voltage field in the electrostatic potential field where there are no vortices, and the fall of voltage in electrical circuits, as well as a voltage that is the EMF (electromotive force). To avoid confusion, the electric field is usually use the term *"potential difference"* for electric circuits - *"voltage drop"*, and for the current sources - *"EMF source"*. When there is no understanding of the differences of definitions, it becomes difficult to understand the essence of complex phenomena in the world of electrical engineering, electronics and automation. What unites these three are related, but still different concepts? First of all, the general point is that all three characterized energetic condition. But then, in answering the question of "energetic condition of what?" Are different. Potential difference characterizes the energy of the electric field potential, the voltage - to plot the electrical circuit, and the EMF source - a energetic characteristic of the device creates an electric current. Commonality in answering the question: "What is it?"and the differences in answering the question "Where?". Everything is known in comparison, so you need to be guided perfectly in all three of the above concepts.

We have some way passed charge **q** from point A to points of B, from the initial capacity to the end, and the difference between them and there is a potential difference. What does this tell us? If **Δφ = φ _{A}-φ_{B}** (potential difference), then to find out what work that has made charge made their way, we need to

**Δφ**multiplied by the amount of charge

**q**, and it is necessary to take into account the sign of the charge.

The resulting value is the work that makes the charge if you move. In other words, the potential energy field is converted into kinetic energy of charge, as well as a charge in the case of movement in the direction of the opposite sign it reduces the field intensity, the potential energy field is reduced.

If some non-Coulomb forces act on the charge, and thus will move it to the side of the field, where the sign is the same as that of the charge, the work will be made with the opposite sign, to be more precise, it will be spent outside the state and the total energy of the field grow. In one case, the potential energy of the field is reduced, due to the fact that some of this energy is converted into kinetic energy, and in another case on the charge against external mechanical forces Coulomb forces - the potential energy increases from an external source. In the first case, the charge moves in the direction of decreasing its energy condition, and in the second case it moves in the direction of increasing its energy condition. Accordingly, the work can either commit with a positive sign or negative.

### Energy of electric field

Suppose that there is a certain amount of space is "filled" by the electric field, that is, is the source of the field and thanks to the long-range, we say that the space is filled with a field. Of course, as a matter no field lines, this imaginary representation in the mind, but in the field of space charge will respond to any manifestation of the Coulomb force. Is it possible to somehow characterize the amount of space energy? Since the electric field is a potential, it is possible to speak of its potential energy.

Suppose that the aforesaid amount of space - a volume **V** in flat capacitor, and the capacitor plates has charge **Q**. Potential difference between the electrodes is **Δφ**, then we can calculate the potential energy electric field using the equation:

This equation on condition that amount of space is a physical vacuum, ie there are no physical particles. If **V** is the volume of the space is filled with the substance, if necessary **ε _{0}** (dielectric constant) multiplied by

**ε**- dielectric constant (substance), which is filled with volume

**V**.

An equation then becomes:

An example is given only for the energy field flat capacitor, this is just one case among many, but it allows you to see the important significant correlation. For example, the equation can be found that the volume of one liter (10^{-3}m^{3}) with a voltage (potential difference) at 10^{7} volts able to stock only a small amount of energy is only 0.44 joules. This value for the vacuum, but there are materials which have a dielectric constant is much greater than unity. For water, this value is 81, and for barium titanate can be up to 10000. Accordingly, the same factor increased stored energy.

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