The potential energy of an electric charge depends on its position in an electric field. Therefore it is expedient to introduce the energy of the electric field. Because the force, acting on a charge q in an electric field, directly proportional to the charge q, the work of the field forces in moving the charge is also directly proportional to the charge q. Therefore, and the potential energy of a charge at an arbitrary point of the electric field is directly proportional to this charge:

P_In = f_Inq. (15.8)

The proportionality factor f_In for each determined point of the field remains constant and can serve as an energy characteristic of the field at this point.

Energy characteristic f of the electric field at a given point is called the field potential at this point. The potential measured by the potential energy of a unit positive charge, located at a given point of the field:

f_In = P_In/q. (15.8and)

The potential of a point electric field is numerically equal to the work, committed by the forces of the field when you move a unit positive charge from that point to infinity.

The potential field at a given point can be calculated theoretically. It is determined by the size and location of charges, creating a field, as well as the environment. Due to the complexity of these calculations here, we do not give. We write only the formula for the potential field of a point charge q, obtained in the result of this calculation.

If the distance from the charge q to the point 1, in which is calculated potential, denoted by r₁ (rice. 15.11), you can show, the potential at this point:

f₁ = q/4пԑ_Cr₁. (15.9)

Note, that formula calculates the potential of the field, created by the charge q, which is uniformly distributed over the surface of the balloon, for all points, outside of the ball. In this case, r₁ denotes the distance from the center of the ball to the point 1. (Think, when calculating according to the formula (15.9) the potential will be positive and when negative.)

You should pay attention to the fact, the potential field of a positive charge decreases as the distance from the charge, but the potential field of a negative charge — increases. Since the potential is a scalar quantity, it, when the field created by many charges, the potential at any field point is equal to the algebraic sum of the potentials, created at this point by each charge separately.

The work of the field forces can be expressed through potential difference. Remember, the work when moving charge q_PR between points 1 and 2 (rice. 15.11) is determined by the formula (15.6and):

A₁₂ = -DP₂₁= -(P₂ - P₁).

Replacing P by its value from formula (15.8), get:

A₁₂ = -(f₂q_PR — f₁q_PR) = -q_PR(f₂— f₁) = — q_PRDF.

Instead of using the increment of the potential is DF= f₂— f₁ the potential difference in the initial and final points of the trajectory f₁— f₂, get:

A₁₂ = q_PR(f₁— f₂).

The potential difference (f₁— f₂) called tension between points 1 and 2 and denoted by U₁₂. Thus:

A₁₂ = q_PRU₁₂

Dropping indexes, get:

A = qU. (15.10)

Therefore, work force field when moving the charge between two points the field is directly proportional to the voltage between those points.

We derive from (15.10) the unit of stress in SI U:

U=A/q=1 j/1 TC=1 j/C=1 kg*m²/(with³*And)=1 In.

The SI unit of voltage volt accepted (In). Volt is the voltage (the potential difference) between two points of the field, in which, moving the charge in 1 TC from one point to another, the field does work in the 1 J.

Note, in practice the charges are always moved between two defined points of the field, so often it is important to know the tension between individual points, rather than their potentials.

From the formula (15.9) see, in all points of the field, located at a distance r₁ from a point charge q (rice. 15.11), the potential f₁ will be the same. All these points lie on the surface of a sphere, described by the radius r₁ from the point, which is a point charge q.

The surface, all of whose points have the same potential, is called equipotential (from the Latin "equi" equal). Sections of such surfaces with potentials f₁ and f₂ for field of a point charge in figure. 15.11 shown by circles. For equipotential surface of the true ratio

ф=const. (15.11)

It turns out, the lines of the electric field is always normal to equipotential surfaces. This means, the work of the field forces in moving a charge on equipotential surface is zero. (Show, this conclusion follows also directly from the formula (15.10).)

Since the work of the field forces in moving the charge depends only on the potential difference between the beginning and the end of the road, moving a charge q from one equipotential surface to another (the potentials are f₁ and f₂) this work does not depend on the shape of the path and equal to A=q( f₁—f₂).

In the future it should be remembered, that under the action of the field forces positive charges always move from larger to smaller potential, and negative Vice versa.