# 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. ${\ displaystyle {\ vec {F}}}$ 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 .