The potential of the electric field, the relationship between strength and potential

Consider the relationship between tension and potential in an electric field. Suppose we have some positively charged body. This body is surrounded by an electric field. We will transfer to this field a positive charge, during the transfer of which the work will be performed. The magnitude of this work is directly proportional to the size of the charge and is dependent on its place of displacement in the field. If we take the ratio of the value of the perfect work A to the value of the transferred charge q, then the magnitude of such an interrelation A / q will not be dependent on the value of the 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 in the field, moving it from an infinitely distant point, whose field strength equals zero. The magnitude of the interrelationship of the work that will have to be performed against the forces of the electric field to the value of the charge that is transferred will depend only on the position of the last point of displacement. As a consequence, this value serves to characterize such a point of the field.

The value, which is measured by the ratio of the work performed when carrying the positive charge to a certain point of the field from infinity, to the value of the charge that moves, is called the field potential.

It is clear from the definition that at a certain point the field potential is equal to the work that takes place when a positive charge moves to a given point from infinity.

The value of the potential is denoted by the letter φ:

Φ = A / q

The potential is scalar. The potentials of each point in the field of a positively charged body have a positive value, and the field potentials of a body with a negative charge have a negative value.

Let us demonstrate that the interrelationship between the magnitude of the work that occurs when a positive charge is transferred to the value of the transferred charge is equal to the difference in the potentials of the displacement points.

The potential difference between 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 strength and the potential is expressed by the equation:

U = φ₁ - φ₂

In this definition, the potential of an infinitely remote point will be zero. In this case, it is said that the point of the zero potential can be an arbitrary point of the field, the choice of which is completely arbitrary. The potential difference of two arbitrary points of the field does not depend on the chosen point of the zero potential.

In theoretical works, the zero point of the potential is an infinitely remote point. And in practice - any point on the earth's surface.

Thus, the potential in physics is a quantity that is measured by the ratio of work when transferring a positive charge from the earth's surface to a certain point of the field to the value of a given charge.

The relationship between strength and potential expresses the characteristic of the electric field. And, if the tension serves as its power characteristic and allows to determine the magnitude of the force that acts on the charge at an arbitrary point of this field, then the potential is its energy characteristic. From the potentials at different points of the electric field, we can determine the magnitude of the work on charge transfer 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, and φ₂ is the potential of the displacement points.

Let us consider the relationship between the strength and the potential in a single-valued electric field. The stress E at any point of such a field is the same, and hence the force F, which acts on a unit of charge, is the same and equals E. It follows that the force that acts on the charge q in a given field will be F = qE.

If the distance between two points of such a field is d, then when the charge moves, work will be done:

A = Fd = gEd = g (φ₁-φ₂),

Where φ₁-φ₂ is the difference between the potentials between the field points.

From here:

E = (φ₁-φ₂) / d,

those. The intensity of a homogeneous electric field will be equal to the potential difference, which per unit length, which is taken along the line of force of a given field.

At short distances, the relationship between the strength and the potential is determined similarly in an inhomogeneous field, since any field between two closely spaced points can be taken as homogeneous.