Conservation of the electric charge

Introduction

The conservation of the electric charge is a physical Principe. It expresses that the electric Charge of a system is a Invariant, i.e. it cannot change, some are the transformations undergone by this system.

Thus, during a chemical reaction, the total sum of the loads of the concerned species is preserved between the produced Réactifs and . In the same way, at the time of a collision between atoms, ions or molecules, of a radioactive decay, or an exchange energy - Matter, it is the same.

Conservation equation of the load in electromagnetism

If $\ vec {J}$ indicates the voluminal Vecteur density of current and $\ rho$ the voluminal Densité of load:

It is a particular case of the matter assessment for a preserved quantity.

It is also consequence of the Maxwell's equations; on the basis of the equation of Maxwell-Amp:

$\ vec {belch} \, \ vec {B} - \ frac {1} {c^ {2}} \, \ frac {\ partial \, \ vec {E}} {\ partial \, T} = \ mu_ {0} \, \ vec {J}$

then by taking the Divergence (knowing that the divergence of a Rotationnel is null):

$- \ frac {1} {c^ {2}} \, \ frac {\ partial \, div \, \ vec {E}} {\ partial \, T} = \ mu_ {0} \, div \, \ vec {J}$

and by finally using the equation of Maxwell-Gauss:

$div \, \ vec {E} = \ mu_ {0} \, c^ {2} \, \ rho$

the announced result is obtained.

Some consequences

In permanent mode, i.e $\ frac {\ partial} {\ partial \, T} =0$ , one has $div \, \ vec {J} =0$ : $\ vec {J}$ is then a zero divergence field. Thus, while integrating on a closed surface, for example a piece of discussion thread, one can find the law of the nodes of Kirchhoff concerning the conservation of the intensity.

only Let us consider a conducting material of homogeneous Conductivité $\ gamma$ in the universe. Conservation equation of the load and Law of Ohm $\ vec {J} = \ gamma \, \ vec {E}$ one draws, $\ gamma$ being supposed homogeneous: $\ gamma \, div \, \ vec {E} + \ frac {\ partial \, \ rho} {\ partial \, T} =0$ . By once again using the equation of Maxwell-Gauss one obtains the temporal evolution of $\ rho$ : $\ frac {\ partial \, \ rho} {\ partial \, T} + \ gamma \, \ mu_ {0} \, c^ {2} \, \ rho=0.$

Thus,

\ rho

tends exponentially towards 0 with a time-constant

\ frac {1} {\ gamma \, \ mu_ {0} \, c^ {2}}

which is about

10^ {- 18} \, s

for a metal of conductivity about

10^7 \, S.m^ {- 1}

: it cannot thus remain of voluminal density of load in a good driver. This can appear paradoxical if the driver had a nonnull total load initially! One can answer it by affirming that this total load is found in the form of a surface Densité of load at the edge of the driver, the voluminal Densité of load inside being quite null.

See too

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