Electric Field theory

The Electric Field is the region of space in which any cargo located at a point in that region undergoes an action or electrical force due to the presence of a load or electrical charges. The most important features of electric charge are:

• The electrical charge is conserved.
• It is quantized, it must be an integer multiple of the fundamental unit of charge, which is the electron charge. QE = 1.602 x10-19 C
• The forces of equal sign are repulsed and forces with opposites signs are attracted.
• The forces between loads are inversely proportional to the square of the distance between them.
• The forces between charges are central character.
• The forces between charges are conservative, ie the work done by them along a closed path is zero.

The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding.

The electric field is a vector field with SI units of Newtons per Coulomb (N/C) or, equivalently, Volts per metre (V/m). The SI base units of the electric field are

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FORMULA SUMMARY:

Coulomb’s constant in the SI

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In the vacuum

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In any other enviroment

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Coulomb’s law

The magnitude of the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance that separates them.

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Given that the value of the constant K is: (ε = Vacuum permittivity constant ; Q = interacting charges ; r = The distance between both charges)

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Electric field intensity

The intensity of the electric field at a point is the force acting on the unit positive charge placed at that point.
The field that creates a point charge Q at each point is:

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Electric potential energy
It is defined as a magnitude which equals the decrease conservative work:

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The electric potential energy between two charges is:

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Lines of force and equipotential surfaces
A power line or flow line is the curve whose tangent line provides the direction of the field at that point.

• The lines of force emerging from the positive charges and enter negative.
• The number of lines of force entering or leaving is proportional to the value of the shits.
• The lines never intersect.
• The line density is proportional to the modulus of the electric field.

The equipotential surfaces are those containing all points of equal power, they are perpendicular to the lines of force.

Gauss’s law

(Φ = electric flux ; E = electric field ; da= vector representing an infinitesimal element of area ; Q = Q is the total charge enclosed within the surface)

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Faraday’s law

(dl = is an infinitesimal vector element of the contour C ; B = the magnetic field ; S = surface bounded by the closed contour C)

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Electric potential due to a point charge

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Electric potential due to a two points charge

(r1 and r2 the distances between the charges q1 and q2 and the point P respectively)

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Electrical potential generated by a discrete distribution of charges

(q = the value of the charge n ; r = the distance to the point)

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Electrical potential generated by a continuous distribution of charges

(dq = differential element of the charge distribution ; r = distance to the point in which it is calculated V ; dV = the potential that dq produces in this point)

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You can download the App BioProfe READER to practice this theory with self-corrected exercises.