Electric field strength

Physical size
Surname Electric field strength
Formula symbol ${\ displaystyle {\ vec {E}}}$
Size and
unit system
unit dimension
SI V · m -1 M · L · I −1 · T −3
Gauss ( cgs ) statV · cm -1 M ½ · L −½ · T −1
esE ( cgs ) statV · cm -1 M ½ · L −½ · T −1
emE ( cgs ) ABV · cm -1 L ½ · M ½ · T

The physical quantity of electrical field strength describes the strength and direction of an electrical field , i.e. the ability of this field to exert force on charges . It is a vector and is defined by at a given point

${\ displaystyle {\ vec {E}} = {\ frac {\ vec {F}} {q}} \,}$.

${\ displaystyle q}$stands for a small test charge that is located at the given location, is the force acting on this test charge. This definition makes sense because of the proportionality of force and charge. ${\ displaystyle {\ vec {F}}}$

The length of the arrows is a measure of the field strength at selected points.

A certain amount and a certain direction of the electric field is assigned to each point in space. In field line pictures , the lines run in the direction of the field at every location, from positive to negative charges; The amount of field strength can be read off from the line density (in the room).

unit

The SI unit of the electric field strength is Newtons per coulomb or volt per meter . The following applies: ${\ displaystyle {\ vec {E}}}$

${\ displaystyle \ mathrm {{\ frac {N} {C}} = {\ frac {J} {C \ cdot m}} = {\ frac {W \, s} {A \, s \ cdot m}} = {\ frac {V \, A \ cdot s} {A \, s \ cdot m}} = {\ frac {V} {m}}}}$

Size concept for the electric field strength

Area Electric field strength E
the atmosphere 100 to 200 V / m
Color television 400 V / m
Dielectric strength of the air 3 MV / m
capacitor 1 to 10 MV / m

Relationship with the electrical flux density

Also used to describe the electric field is the electric flux density , formerly also called displacement density , which is linked to the electric field strength via the material equations . The relationship applies in a vacuum ${\ displaystyle {\ vec {D}}}$${\ displaystyle {\ vec {E}}}$

${\ displaystyle {\ vec {D}} = \ varepsilon _ {0} {\ vec {E}}}$

with the electric field constant . ${\ displaystyle \ varepsilon _ {0}}$

Connection with the potential

In many cases, the electric field strength can be calculated using the associated potential . In the context of electrostatics, the electric field strength is equal to the negative gradient of the (scalar) electric potential : ${\ displaystyle \ Phi}$

${\ displaystyle {\ vec {E}} ({\ vec {r}}) = - \ nabla \ Phi ({\ vec {r}})}$

The corresponding more general equation of electrodynamics also takes into account the vector potential and the time dependence: ${\ displaystyle {\ vec {A}}}$

${\ displaystyle {\ vec {E}} ({\ vec {r}}, t) = - \ nabla \ Phi ({\ vec {r}}, t) - {\ frac {\ partial} {\ partial t }} {\ vec {A}} ({\ vec {r}}, t)}$

literature

• Adolf J. Schwab: Conceptual world of field theory: practical, clear introduction. Electromagnetic fields, Maxwell's equations, gradient, rotation, divergence . 6th edition. Springer, Berlin 2002, ISBN 3-540-42018-5 .