Chapter 4-1 Gauss's Law

 

1. 가우스 법칙 : charge와 일(힘, electric field intensity, E)이 어떤관계가 있느냐 를 알아보는 법칙 (조건 : 임의의 전하를 둘러싼 폐곡면에 관한 법칙이다)

 

2. Intergral form of the Gauss's Law : Total charge(q) enclsed by a closed surface (S) is equal to the surface integral of electric flux density(D ) produced by the charge. (의미 : q가 둘러싼 폐곡면에 대해서 q로 인한 electric field intensity(E ) 또는 flux density(D ) 를 면적분 해준 값은 q 그 자신이 된다 -> q로 인해 이 field 가 생겼으므로 당연한 것, q가 힘을내서 일을하면 그 일의 전체합은 q가 된다 ->q는 에너지의 source 라는 것을 알 수 있다. )

 

3. Meaning of the Gauss's Law : Gauss's Law directly shows us the CHARGE CONSERVATION within a closed surface. Furthermore, since a charge q is an energy source, this Gauss's low implicate A KIND OF Energy Consevation : +q를 발생시키는 electric field intensity E (단위전하에 미친 힘) 를 생각해보자. E는 매질을 진행할텐데 매질을 등방성 (사방으로 퍼져나간다)으로 가정해보자. 전하 q가 +1C(unit charge)에 미치는 힘을 E 라고 하는데, 이 힘으로 인해 unit charge (da에 있는) 가 unit distance 만큼 밀린다고 하면 그만큼 일을 한 것이 된다. 이때 전체 표면만큼을(S) 다 더하면(da를 적분하면), total work는 q가 된다. The force (+1)E would apply to the unit charge and move it outward throughout the whole surface enclosing the charge(+q). If this force (+1)E to move the unit charge (+1) by a unit distance (+1), then the whole work done by this force throughout the whole closed surface would be summation of (+1)E (+1) .

 

4. The actual electric force experienced by a unit charge would be different depending on the medium where the charge is located like a force experience within waterpool vs a force in the air. So the electrial property of the medium should be included such that if the electrical resistance (ε) of the medium against E is strong (ε is big), then the actual/net forve experienced by a charge within this medium would be smaller/less than within the medium with weak resistanve (ε is small) . Thus, D = ε0E  is the electric flux density, which is independent of the medium property, while E is dependent upon the property (ε0) of the medium.