The work of the electric field on charge transfer

Any force that is in an electric field is affected by force. In this connection, when the charge moves in the field, a certain work of the electric field takes place. How to calculate this work?

The work of the electric field consists in the transfer of electric charges along the conductor. It will be equal to the product of voltage, current and time spent on work.

Applying the formula of Ohm's law, we can obtain several different variants of the formula for calculating the operation of the current:

A = U˖I˖t = I²R˖t = (U² / R) ˖t.

In accordance with the law of conservation of energy, the work of the electric field is equal to the change in the energy of an individual part of the chain, and therefore the energy released by the conductor will be equal to the work of the current.

Let's express in the SI system:

[A] = В˖А˖с = Вт˖с = J

1 kWh = 3,600,000 J.

We will make an experiment. Let us consider the movement of a charge in the field of the same name, which is formed by two parallel plates A and B and charged charges of opposite charges. In this field, the lines of force are perpendicular to these plates throughout their length, and when plate A is positively charged, then the field strength E will be directed from A to B.

Suppose that the positive charge q moves from point a to point b along an arbitrary path ab = s.

Since the force that acts on the charge that is in the field will be equal to F = qE, then the work done when the charge moves in the field according to the given path will be determined by the equality:

A = Fs cos α, or A = qFs cos α.

But s cos α = d, where d is the distance between the plates.

Hence follows: A = qEd.

Suppose now the charge q moves from a and b to acb in essence. The work of the electric field, accomplished on this path, is equal to the sum of the work done on its separate sections: ac = s₁, cb = s₂, i.e.

A = qEs₁ cos α₁ + qEs₂ cos α₂,

A = qE (s₁ cos α₁ + s₂ cos α₂,).

But s₁ cos α₁ + s₂ cos α₂ = d, and hence, in this case, A = qEd.

In addition, assume that the charge q moves from a to b along an arbitrary curve of the line. To calculate the work done on a given curvilinear path, it is necessary to layer the field between the plates A and B by a number of parallel planes that are so close to each other that individual sections of the path s between these planes can be considered straight lines.

In this case, the work of the electric field produced on each of these path segments will equal A₁ = qEd₁, where d₁ is the distance between two contiguous planes. And the total work along the entire path d will be equal to the product qE and the sum of distances d₁ equal to d. Thus, and as a result of the curvilinear path, the perfect work will be equal to A = qEd.

The examples considered by us show that the work of an electric field on the transfer of a charge from any point to another does not depend on the shape of the path of movement, but depends solely on the position of these points in the field.

In addition, we know that the work done by the force of gravity when the body moves along an inclined plane having a length l will be equal to the work done by the body when it falls from a height h and the height of the inclined plane. Hence, the work of gravity, or, in particular, work when the body moves in the gravity field, also does not depend on the shape of the path, but depends only on the difference in heights of the first and last points of the path.

So it can be shown that such an important property can possess not only a homogeneous, but also every electric field. A similar property is possessed by gravity.

The work of the electrostatic field on the displacement of a point charge from one point to another is determined by a linear integral:

A₁₂ = ∫ L₁₂q (Edl),

Where L₁₂ is the trajectory of the charge motion, dl is an infinitesimal displacement along the trajectory. If the contour is closed, then the symbol для is used for the integral; In this case it is assumed that the direction of circuit bypass is selected.

The work of electrostatic forces does not depend on the shape of the path, but only on the coordinates of the first and last points of displacement. Consequently, the field strengths are conservative, and the field itself is potentially. It is worth noting that the work of any conservative force along a closed path will be zero.