高斯定律和平方反比有什么区别?


回答 1:

TheinversesquarelawsimplysaysthatsomethinggetssmallerinproportiontoR2.Itsaysnothingelse.Therearemanydifferentthingsthatfollowsuchalaw.The inverse square law simply says that something gets smaller in proportion to R^2. It says nothing else. There are many different things that follow such a law.

高斯定律有积分形式和微分形式。这些是

SDds=Vρvdv\oint_S \vec{D} \bullet d \vec{s} = \int_V \rho_v dv

D=ρv\nabla \bullet \vec{D} = \rho_v

我认为您所指的方程式是上述高斯定律的结果,并且是围绕点电荷的场。

D=Q4πR2a^R\vec{D} = \frac{Q}{4 \pi R^2} \hat{a}_R

Thereisalotmoreherethanjustthe1/R2relation.Itisavectorequationandalsoincorporatescharge[math]Q[/math].Thefactor[math]4πR2[/math]isthefieldenergyspreadingitselfoutoverasphereofradius[math]R[/math].There is a lot more here than just the 1/R^2 relation. It is a vector equation and also incorporates charge [math]Q[/math]. The factor [math]4 \pi R^2[/math] is the field energy spreading itself out over a sphere of radius [math]R[/math].