Main concepts. Electric field is usually described by two basic quantities – vector of electric intensity and electric potential

Electric field is usually described by two basic quantities – vector of electric intensity and electric potential

; ,

where – force acted with a test point charge q₀, which is located in the given point of a field; W_n – potential energy of a charge q₀ , in the given point.

Intensity and potential of electric fieldof the point charge q at a distance of r of the charge

; ,

where e₀ = 8, 85 × 10^–12 F / m – permittivity of vacuum; e – relative permittivity of medium (for air e=1).

For the uniform field the dependence between the intensity and potential of the electric field

,

where r _{1, 2} – the distance between equipotential lines with the potentials j₁ and j₂, E – the electric intensity in the middle of the equipotential lines with the potentials j₁ and j₂.

The modulus of electric field intensity:

1) uniformly charged sphere with a radius of R at a distance of r from the centre of sphere

а) E = 0, for r < R;

б) , for r ³ R,

where Q= s × S – a charge of sphere, s – surface charge density of sphere (charge of 1 m ² of a surface), S= 4p R² – surface area of sphere.

2) endless uniformly charged cylinder with a radius of R at a distance of r from the axis of the cylinder.

а) E = 0, for r < R;

б) for r ³ R,

where Q= t × L – a charge of cylinder, t – linear charge density (charge of 1 m of a length), L – length of cylinder.

3) endless uniformly charged plate

The superposition principle: the electric field created by one charge is independent from positions of other charges. Then the resultant vector is a vector sum of vectors of electric field individual charges:

,

therefore:

a) the direction of the resultant vector is defined by parallelogram rule of the vectors’ additions (see example 1);

b) the magnitude of the resultant vector is defined by cosine theorem:

,

where a – angle between vectors.

The electrostatic force acting on a test charge q

F=q × E _RES.