6. Use the differential form of Gauss's law to determine the static charge density p(x, y, z) in a region

of space if:

a) The static displacement field in the region is specified as D(x, y, z) = -6sgn(z)2 C/m². Describe

the nature of the charge density "in words"- do we find a volumetric distribution of charge, or

a surface charge, or a line charge? Hint: how do we express the derivative of a sgn function?

b) The static displacement field in the region is specified as

-216 C/m²,

D(x, y, z)=24z C/m²,

216 C/m²,

z<-4m,

|z| < 4m,

z > 4m.