Simple Nature - Light and Matter

The symmetry between the two sides could be broken by the

existence of other charges nearby, whose fields would add onto the

field of the surface itself. Even then, Gauss’s law still guarantees

4 πkqin= (E 1 −E 2 )·A 1 ,

or

|E⊥,1−E⊥,2|= 4πkσ,

where the subscript⊥indicates the component of the field parallel

to the surface (i.e., parallel to the area vectors). In other words,

the electric field changes discontinuously when we pass through a

charged surface; the discontinuity occurs in the component of the

field perpendicular to the surface, and the amount of discontinuous

change is 4πkσ. This is a completely general statement that is true

near any charged surface, regardless of the existence of other charges

nearby.

650 Chapter 10 Fields