Consider the relationship between tension and potential in an electric field. Let's say we have some kind of positively charged body. This body is surrounded by an electric field. We transfer to this field a positive charge, during the transfer of which work will be performed. The magnitude of this work is directly proportional to the size of the charge and depends on its place of movement in the field. If we take the ratio of the magnitude of the perfect work A to the magnitude of the transferred charge q, then the magnitude of this relationship A / q will not depend on the amount of charge that is transferred, but will depend only on the choice of displacement points, and the shape of the path does not matter.
We introduce a charge into the field, moving it from an infinitely distant point, the field strength of which is zero. The magnitude of the relationship of the work that will have to be done against the forces of the electric field to the amount of charge that is transferred will depend only on the position of the last displacement point. As a consequence of this, such a quantity serves to characterize such a point of the field.
The value that is measured by the ratio of the work performed when a positive charge is transferred to a certain point in the field from infinity to the amount of charge that moves is called the field potential.
It can be seen from the definition that, at a certain point, the field potential is equal to the work that is done when a positive charge moves to a given point from infinity.
The potential value is denoted by the letter φ:
φ = A / q
Potential is a scalar quantity. The potentials of each point of the field of a positively charged body have a positive value, and the potentials of the field of a body with a negative charge have a negative value.
We demonstrate that the relationship between the magnitude of the work that is accomplished during the transfer of a positive charge and the magnitude of the transferred charge is equal to the potential difference of the displacement points.
The potential difference of two different points of the field, in this case, is called the field strength between such points. If the field voltage is denoted by the letter U, then the relationship between the intensity and potential is expressed using the equation:
U = φ₁ - φ₂
In this definition, the potential of an infinitely distant point will be zero. In this case, they say that an arbitrary point of the field can be a point of zero potential, its choice is completely conditional. The potential difference of two arbitrary points of the field does not depend on the selected point of zero potential.
In theoretical works, the zero point of potential is an infinitely distant point. But in practice - any point on the earth's surface.
Thus, the potential in physics is a quantity that is measured by the ratio of the work when a positive charge is transferred from the earth's surface to a certain point in the field to the magnitude of a given charge.
The relationship between intensity and potential expresses the characteristic of the electric field. Moreover, if the tension serves as its strength characteristic and allows you to determine the magnitude of the force that acts on the charge at an arbitrary point in this field, then the potential is its energy characteristic. By potentials at various points of the electric field, we can determine the magnitude of the work on moving the charge using the formulas:
A = qU, or A = q (φ₁ - φ₂),
where q is the magnitude of the charge, U is the voltage between the field points and φ₁, φ₂ is the potential of the displacement points.
Consider the relationship between intensity and potential in a unique electric field. The tension E at any point of such a field is the same, and therefore the force F, which acts on a unit of charge, is also the same and is equal to E. It follows from this that the force that acts on a charge q in this field will be F = qE.
If the distance between two points of such a field is d, then when the charge moves, the work will be done:
A = Fd = gEd = g (φ₁-φ₂),
where φ₁-φ₂ is the potential difference between the points of the field.
From here:
E = (φ₁-φ₂) / d,
those. the intensity of a uniform electric field will be equal to the potential difference, which is per unit of length, which was taken along the field line of this field.
At small distances, the relationship between tension and potential is determined similarly in an inhomogeneous field, since any field between two closely spaced points can be mistaken for a uniform one.