on any charge, which is in an electric field, the force acts.In this regard, the movement of charge in a field is defined by operation of the electric field.How to calculate this work?
work of the electric field is to transfer electrocharge along the conductor.It will be equal to the product of voltage, current and time spent on the job.
apply formulas Ohm's law, we can have several different variants of the formula for calculation of the current work:
A = U˖I˖t = I²R˖t = (U² / R) ˖t.
in accordance with the law of conservation of energy operation of the electric field equals the change in the energy of a single section of the circuit, and therefore the energy released by the conductor, will be equal to the current.
express SI:
[A] = = V˖A˖s Vt˖s = J.
kVt˖chas 1 = 3600000 George.
draw experience.Consider the movement of charge in the same field, which is formed by two spaced parallel plates A and B and charged with opposite charges.In this field the lines of force throughout its length perpendicular to these plates, and when the plate A is positively charged, then the intensity of the field E is directed from A to B.
assume that the positive charge q moved from point a to point b in an arbitrary wayab = s.
Since the force which acts on the charge, which is in the field will be equal to F = qE, the work done when moving charge in the field according to a predetermined path defined by the equation:
A = Fs cos α, or A =qFs cos α.But
s cos α = d, where d - the distance between the plates.
It follows: A = qEd.
Let us now move the charge q of a and b in fact acb.The work of the electric field, done in this way, is the sum of the work done in some areas it: ac = s₁, cb = s₂, ie
A = qEs₁ cos α₁ + qEs₂ cos α₂,
A = qE (s₁ cos α₁ + s₂ cos α₂,).
But s₁ cos α₁ + s₂ cos α₂ = d, and therefore in this case A = qEd.
Also, assume that the charge q moves from a to b is an arbitrary curve.To calculate the work done on this curved path, it is necessary to stratify the field between the plates A and B by a number of parallel planes that are so close to each other that some parts of the path s between the planes can be considered straight.
In this case, operation of the electric field generated in each of these segments of the path will be A₁ = qEd₁, where d₁ - the distance between two adjacent planes.A total work all the way d will be equal to the sum of the product of qE and distances d₁, equal to d.Thus, as a result of the curved path the perfect job will be A = qEd.
examples considered above indicate that the operation of the electric field to move the charge from any point to another is independent of the form of the path of movement, and depends solely on the position of the data points in the field.
In addition, we know that the work that is done by gravity when moving a body on an inclined plane having a length l, will be equal to the work that makes the body of a fall from a height h, and the height of the inclined plane.Hence, operation of gravity or, in particular, the work by moving the body in the gravitational field, too, does not depend on the shape of the path and depends only on the difference in height between the first and last points of the path.
So we can prove that this important feature can have not only homogeneous, but also all the electric field.Similarly, the property and has the force of gravity.
work of the electrostatic field of a point charge moving from one point to another is determined by the line integral:
A₁₂ = ∫ L₁₂q (Edl),
where L₁₂ - the trajectory of the charge, dl - an infinitesimal displacement along the trajectory.If the path is closed, it is used for the integral symbol ∫;in this case it is assumed that the contour line is selected.Employment
electrostatic force does not depend on the shape of the path, but only on the coordinates of the first and last points of displacement.Consequently, conservative force field, and the field itself - potentially.It is worth noting that the work of any conservative force along a closed path is zero.
